arXiv subjects

Shiraz Minwalla

Publications and source records attributed to Shiraz Minwalla.

At least 19 recordsLinked to original sources

arXiv2026

From $Z$ to $a$: High-temperature relations, subleading semi-universality, and conformal anomalies

The free energy of any CFT, $ \ln Z(\beta; \omega_i)$, admits two expansions: high temperature ($\beta \rightarrow 0$) and fast rotation ($\omega_i \rightarrow 1$). We demonstrate that locality of the thermal effective action forces $\ln Z$ to take a simple analytic form at all orders in the high temperature expansion, and further imposes an infinite number of sharp relations on the coefficients in this expansion. All are homogeneous, except at order $\beta^1$ due to the Weyl anomaly. From this, the $a$-anomaly can be extracted from the partition function. The relations resum in the fast-spinning expansion into differential equations in $\beta$ obeyed by the semi-universal limit and its corrections. We verify the relations in a variety of CFTs. We generalize to any even $d$, but find no similar relations at odd $d$.

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arXiv2025

Semi-universality of CFT$_d$ entropy at large spin

The thermal partition function, $Z$, of a $CFT_d$ on $S^{d-1}$ is parameterized by the inverse temperature $\beta$ along with $\lfloor d/2\rfloor$ angular velocities $\omega_i$. In this paper, we investigate the behaviour of this partition function when $n$ of the $\omega_i$ are scaled to unity (the largest allowed value) at fixed values of the other $(\lfloor d/2\rfloor-n)$ angular velocities. We argue that $\ln Z$ develops a simple pole in $(1-\omega_i)$ for each $\omega_i$ that is scaled to unity. The residue of this product of poles is a theory dependent (so non-universal) function of $\beta$ and the fixed angular velocities. The inverse Laplace transformation of this partition function constrains the functional form of the field theory entropy as a function of charges in a limit in which angular momenta and the twist are scaled as follows. While $n$ special angular momenta $J_1\ldots J_n$ are scaled to infinity, the twist and the other angular momenta - collectively denoted $x_i$ - are also taken to infinity but at the slower rate that ensures that the scaled charges $x_i/(J_1 J_2 \ldots J_n)^{\frac{1}{n+1}}$ are held fixed. In this limit, we demonstrate that the scaled entropy $S/(J_1 J_2 \ldots J_n)^{\frac{1}{n+1}}$ depends only on the $\lfloor d/2\rfloor-n+1$ scaled charges defined above (the precise form of this dependence is non-universal). We verify our predictions (and compute all non-universal functions) in the case of free scalar theories (which show surprisingly rich behaviour) as well as large $N$, strongly coupled ${\cal N}=4$ Yang Mills theory. The last theory is analyzed in the bulk via the AdS/CFT correspondence. In the scaling limit described above, its phase diagram displays sharp phase transitions between black hole, grey galaxy, and thermal gas phases.

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arXiv2025

Monodromies of CFT correlates on the Lorentzian Cylinder

While correlators of a CFT are single valued in Euclidean Space, they are multi valued -- and have a complicated sheet structure -- in Lorentzian space. Correlators on $R^{1,1}$ are well known to access a finite number of these sheets. In this paper we demonstrate the spiral nature of lightcones on $S^1 \times $ time allows time ordered correlators of a $CFT_2$ on this spacetime -- the Lorentzian cylinder -- to access an infinite number of sheets of the correlator. We present a complete classification, both of the sheets accessed as well as of the various distinct causal configurations that lie on a particular sheet. Our construction provides a physical interpretation for an infinite number of sheets of the correlator, while, however, leaving a larger infinity of these sheets uninterpreted.

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arXiv2025

Supersymmetric Grey Galaxies, Dual Dressed Black Holes and the Superconformal Index

Motivated by the recent construction of grey galaxy and Dual Dressed Black Hole solutions in $AdS_5\times S^5$, we present two conjectures relating to the large $N$ entropy of supersymmetric states in ${\cal N}=4$ Yang-Mills theory. Our first conjecture asserts the existence of a large number of supersymmetric states which can be thought of as a non interacting mix of supersymmetric black holes and supersymmetric `gravitons'. It predicts a microcanonical phase diagram of supersymmetric states with eleven distinct phases, and makes a sharp prediction for the supersymmetric entropy (as a function of 5 charges) in each of these phases. The microcanonical version of the superconformal index involves a sum over states - with alternating signs - over a line in 5 parameter charge space. Our second (and more tentative) conjecture asserts that this sum is dominated by the point on the line that has the largest supersymmetric entropy. This conjecture predicts a large $N$ formula for the superconformal index as a function of indicial charges, and predicts a microcanonical indicial phase diagram with nine distinct phases. It predicts agreement between the superconformal index and black hole entropy in one phase (so over one range of charges), but disagreement in other phases (and so at other values of charges). We compare our predictions against numerically evaluated superconformal index at $N\leq10$, and find qualitative agreement.

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arXiv2024

Grey Galaxies in $AdS_5$

It has recently been conjectured \cite{Kim:2023sig} that the end point of the rotational superradiant instability of black holes in $AdS_4$ is a Grey Galaxy: an $\omega=1$ black hole sitting at the centre of $AdS_4$, surrounded by a large disk of rapidly rotating gravitons and other bulk fields. In this paper we study Grey Galaxies in $AdS_5$. In this case, the rotational group is of rank 2, and so has two distinct angular velocities $\omega_1$ and $\omega_2$. We demonstrate that $AdS_5$ hosts two qualitatively distinct Grey Galaxy phases: the first with either $\omega_1\approx 1$ or $\omega_2\approx 1$, and the second with both angular velocities $\approx 1$. We use these results to present a conjecture for a part of the phase diagram of ${\cal N}=4$ Yang-Mills (as a function of energy and the two angular momenta) that displays several phase transitions between regular black holes and various Grey Galaxy phases. We present an explicit gravitational construction of the phases in which $\omega_1$ and $\omega_2$ are both parametrically close to unity, and demonstrate that the corresponding boundary stress tensor is the sum of two pieces. The first is the stress tensor of the central black hole. The second - the contribution of the bulk gas - takes the form of the stress tensor of an equilibrated boundary conformal fluid, rotating at the given angular speeds $\omega_i$. We also briefly comment on the structure of Grey Galaxies in $AdS_D$ for $D > 5$.

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arXiv2024

Dual Dressed Black Holes as the end point of the Charged Superradiant instability in ${\cal N} = 4$ Yang Mills

Charged Black holes in $AdS_5 \times S^5$ suffer from superradiant instabilities over a range of energies. Hairy black hole solutions (constructed within gauged supergravity) have previously been proposed as endpoints to this instability. We demonstrate that these hairy black holes are themselves unstable to the emission of large dual giant gravitons. We propose that the endpoint to this instability is given by Dual Dressed Black Holes (DDBH)s; configurations consisting of one, two, or three very large dual giant gravitons surrounding a core $AdS$ black hole with one, two, or three $SO(6)$ chemical potentials equal to unity. The dual giants each live at $AdS$ radial coordinates of order $\sqrt{N}$ and each carry charge of order $N^2$. The large separation makes DDBHs a very weakly interacting mix of their components and allows for a simple computation of their thermodynamics. We conjecture that DDBHs dominate the phase diagram of ${\cal N}=4$ Yang-Mills over a range of energies around the BPS plane, and provide an explicit construction of this phase diagram, briefly discussing the interplay with supersymmetry. We develop the quantum description of dual giants around black hole backgrounds and explicitly verify that DDBHs are stable to potential tunneling instabilities, precisely when the chemical potentials of the core black holes equal unity. We also construct the 10-dimensional DDBH bulk solutions.

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arXiv2023

The S-matrix and boundary correlators in flat space

We consider the path integral of a quantum field theory in Minkowski spacetime with fixed boundary values (for the elementary fields) on asymptotic boundaries. We define and study the corresponding boundary correlation functions obtained by taking derivatives of this path integral with respect to the boundary values. The S-matrix of the QFT can be extracted directly from these boundary correlation functions after smearing. We interpret this relation in terms of coherent state quantization and derive the constraints on the path-integral as a function of boundary values that follow from the unitarity of the S-matrix. We then study the locality structure of boundary correlation functions. In the massive case, we find that the boundary correlation functions for generic locations of boundary points are dominated by a saddle point which has the interpretation of particles scattering in a small elevator in the bulk, where the location of the elevator is determined dynamically, and the S-matrix can be recovered after stripping off some dynamically determined but non-local ``renormalization'' factors. In the massless case, we find that while the boundary correlation functions are generically analytic as a function on the whole manifold of locations of boundary points, they have special singularities on a sub-manifold, points on which correspond to light-like scattering in the bulk. We completely characterize this singular scattering sub-manifold, and find that the corresponding residues of the boundary correlations at these singularities are precisely given by S-matrices. This analysis parallels the analysis of bulk-point singularities in AdS/CFT and generalizes it to the case of multi-bulk point singularities.

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arXiv2023

The free energy of the large-$N$ fermionic Chern$\unicode{x2013}$Simons theory in the 'temporal' gauge

Most of the computational evidence for the Bose$\unicode{x2013}$Fermi duality of fundamental fields coupled to $U(N)$ Chern$\unicode{x2013}$Simons theories originates in large-$N$ calculations performed in the light-cone gauge. This gauge is ill-suited to computations in curved spacetimes, like the evaluation of the partition function on $\Sigma_g\times S^1$ for arbitrary genus $g$. In this paper, we use another gauge, the 'temporal' gauge, to set up the computation of this partition function. In the large-$N$ limit, and the special case $\Sigma_g=\mathbb{R}^2$, we take the computation through to the end by setting up and solving the gap equations, generalizing tricks explored in arXiv:1410.0558 to finite temperature. Our final results are in perfect agreement with earlier light-cone gauge results, providing a consistency check of both the formalism developed in this paper as well as previously performed light-cone gauge computations. In a follow-up paper, we will report on using our formalism to explicitly compute the partition function on $S^2 \times S^1$ for a finite-sized sphere.

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arXiv2023

'Grey Galaxies' as an endpoint of the Kerr-AdS superradiant instability

Kerr-AdS$_{d+1}$ black holes for $d\geq 3$ suffer from classical superradiant instabilities over a range of masses above extremality. We conjecture that these instabilities settle down into Grey Galaxies (GGs) - a new class of coarse-grained solutions to Einstein's equations which we construct in $d=3$. Grey Galaxies are made up of a black hole with critical angular velocity $ω=1$ in the `centre' of $AdS$, surrounded by a large flat disk of thermal bulk gas that revolves around the centre of $AdS$ at the speed of light. The gas carries a finite fraction of the total energy, as its parametrically low energy density and large radius are inversely related. GGs exist at masses that extend all the way down to the unitarity bound. Their thermodynamics is that of a weakly interacting mix of Kerr-AdS black holes and the bulk gas. Their boundary stress tensor is the sum of a smooth `black hole' contribution and a peaked gas contribution that is delta function localized around the equator of the boundary sphere in the large $N$ limit. We also construct another class of solutions with the same charges; `Revolving Black Holes (RBHs)'. RBHs are macroscopically charged $SO(d,2)$ descendants of AdS-Kerr solutions, and consist of $ω=1$ black holes revolving around the centre of $AdS$ at a fixed radial location but in a quantum wave function in the angular directions. RBH solutions are marginally entropically subdominant to GG solutions and do not constitute the endpoint of the superradiant instability. Nonetheless, we argue that supersymmetric versions of these solutions have interesting implications for the spectrum of supersymmetric states in, e.g. ${\cal N}=4$ Yang-Mills theory.

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arXiv2022

Crossing Symmetry in Matter Chern-Simons Theories at finite $N$ and $k$

We present a conjecture for the crossing symmetry rules for Chern-Simons gauge theories interacting with massive matter in $2+1$ dimensions. Our crossing rules are given in terms of the expectation values of particular tangles of Wilson lines, and reduce to the standard rules at large Chern-Simons level. We present completely explicit results for the special case of two fundamental and two antifundamental insertions in $SU(N)_k$ and $U(N)_k$ theories. These formulae are consistent with the conjectured level-rank, Bose-Fermi duality between these theories and take the form of a $q=e^{\frac{ 2 πi }κ}$ deformation of their large $k$ counterparts. In the 't Hooft large $N$ limit our results reduce to standard rules with one twist: the $S$-matrix in the singlet channel is reduced by the factor $\frac{\sin πλ}{πλ} $ (where $λ$ is the 't Hooft coupling), explaining `anomalous' crossing properties observed in earlier direct large $N$ computations.

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arXiv2022

The Hilbert Space of large $N$ Chern-Simons matter theories

We demonstrate that the known expressions for the thermal partition function of large $N$ Chern-Simons matter theories admit a simple Hilbert space interpretation as the partition function of an associated ungauged large $N$ matter theory with one additional condition: the Fock space of this associated theory is projected down to the subspace of its \emph{quantum} singlets i.e.~singlets under the Gauss law for Chern-Simons gauge theory. Via the Chern-Simons / WZW correspondence, the space of quantum singlets are equivalent to the space of WZW conformal blocks. One step in our demonstration involves recasting the Verlinde formula for the dimension of the space of conformal blocks in $SU(N)_k$ and $U(N)_{k,k'}$ WZW theories into a simple and physically transparent form, which we also rederive by evaluating the partition function and superconformal index of pure Chern-Simons theory in the presence of Wilson lines. A particular consequence of the projection of the Fock space of Chern-Simons matter theories to quantum (or WZW) singlets is the `Bosonic Exclusion Principle': the number of bosons occupying any single particle state is bounded above by the Chern-Simons level. The quantum singlet condition (unlike its Yang-Mills Gauss Law counterpart) has a nontrivial impact on thermodynamics even in the infinite volume limit. In this limit the projected Fock space partition function reduces to a product of partition functions, one for each single particle state. These single particle state partition functions are $q$-deformations of their free boson and free fermion counterparts and interpolate between these two special cases. We also propose a formula for the large $N$ partition function that is valid for arbitrary finite volume of the spatial $S^2$ and not only at large volume.

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arXiv2021

Bounds on Regge growth of flat space scattering from bounds on chaos

We study four-point functions of scalars, conserved currents, and stress tensors in a conformal field theory, generated by a local contact term in the bulk dual description, in two different causal configurations. The first of these is the standard Regge configuration in which the chaos bound applies. The second is the `causally scattering configuration' in which the correlator develops a bulk point singularity. We find an expression for the coefficient of the bulk point singularity in terms of the bulk S matrix of the bulk dual metric, gauge fields and scalars, and use it to determine the Regge scaling of the correlator on the causally scattering sheet in terms of the Regge growth of this S matrix. We then demonstrate that the Regge scaling on this sheet is governed by the same power as in the standard Regge configuration, and so is constrained by the chaos bound, which turns out to be violated unless the bulk flat space S matrix grows no faster than $s^2$ in the Regge limit. It follows that in the context of the AdS/CFT correspondence, the chaos bound applied to the boundary field theory implies that the S matrices of the dual bulk scalars, gauge fields, and gravitons obey the Classical Regge Growth (CRG) conjecture.

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arXiv2020

Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle

We generalize previously obtained results for the (all orders in the 't Hooft coupling) thermal free energy of bosonic and fermionic large $N$ Chern-Simons theories with fundamental matter, to values of the chemical potential larger than quasiparticle thermal masses. Building on an analysis by Geracie, Goykhman and Son, we present a simple explicit formula for the occupation number for a quasiparticle state of any given energy and charge as a function of the temperature and chemical potential. This formula is a generalization to finite 't Hooft coupling of the famous occupation number formula of Bose-Einstein statistics, and implies an exclusion principle for Chern-Simons coupled bosons: the total number of bosons occupying any particular state cannot exceed the Chern-Simons level. Specializing our results to zero temperature we construct the phase diagrams of these theories as a function of chemical potential and the UV parameters. At large enough chemical potential, all the bosonic theories we study transit into a compressible Bose condensed phase in which the runaway instability of free Bose condensates is stabilized by the bosonic exclusion principle. This novel Bose condensate is dual to - and reproduces the thermodynamics of - the fermionic Fermi sea.

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arXiv2020

Classification of all 3 particle S-matrices quadratic in photons or gravitons

We explicitly construct every kinematically allowed three particle graviton-graviton-$P$ and photon-photon-$P$ S-matrix in every dimension and for every choice of the little group representation of the massive particle $P$. We also explicitly construct the spacetime Lagrangian that generates each of these couplings. In the case of gravitons we demonstrate that this Lagrangian always involves (derivatives of) two factors of the Riemann tensor, and so is always of fourth or higher order in derivatives. This result verifies one of the assumptions made in the recent preprint \cite{Chowdhury:2019kaq} while attempting to establish the rigidity of the Einstein tree level S-matrix within the space of local classical theories coupled to a collection of particles of bounded spin.

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arXiv2019

Classifying and constraining local four photon and four graviton S-matrices

We study the space of all kinematically allowed four photon and four graviton S-matrices, polynomial in scattering momenta. We demonstrate that this space is the permutation invariant sector of a module over the ring of polynomials of the Mandelstam invariants $s$, $t$ and $u$. We construct these modules for every value of the spacetime dimension $D$, and so explicitly count and parameterize the most general four photon and four graviton S-matrix at any given derivative order. We also explicitly list the local Lagrangians that give rise to these S-matrices. We then conjecture that the Regge growth of S-matrices in all physically acceptable classical theories is bounded by $s^2$ at fixed $t$. A four parameter subset of the polynomial photon S-matrices constructed above satisfies this Regge criterion. For gravitons, on the other hand, no polynomial addition to the Einstein S-matrix obeys this bound for $D \leq 6$. For $D \geq 7$ there is a single six derivative polynomial Lagrangian consistent with our conjectured Regge growth bound. Our conjecture thus implies that the Einstein four graviton S-matrix does not admit any physically acceptable polynomial modifications for $D\leq 6$. A preliminary analysis also suggests that every finite sum of pole exchange contributions to four graviton scattering also such violates our conjectured Regge growth bound, at least when $D\leq 6$, even when the exchanged particles have low spin.

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arXiv2019

The large $N$ phase diagram of ${\cal N}=2$ $SU(N)$ Chern-Simons theory with one fundamental chiral multiplet

We study the theory of a single fundamental fermion and boson coupled to Chern-Simons theory at leading order in the large $N$ limit. Utilizing recent progress in understanding the Higgsed phase in Chern-Simons-Matter theories, we compute the quantum effective potential that is exact to all orders in the 't Hooft coupling for the lightest scalar operator of this theory at finite temperature. Specializing to the zero temperature limit we use this potential to determine the phase diagram of the large $N$ ${\cal N}=2$ supersymmetric theory with this field content. This intricate two dimensional phase diagram has four topological phases that are separated by lines of first and second order phase transitions and includes special conformal points at which the infrared dynamics is governed by Chern-Simons theory coupled respectively to free bosons, Gross-Neveu fermions, and to a theory of Wilson-Fisher bosons plus free fermions. We also describe the vacuum structure of the most general ${\cal N} = 1$ supersymmetric theory with one fundamental boson and one fundamental fermion coupled to an $SU(N)$ Chern-Simons gauge field, at arbitrary values of the 't Hooft coupling.

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arXiv2019

Matter Chern Simons Theories in a Background Magnetic Field

We study large $N$ 2+1 dimensional fermions in the fundamental representation of an $SU(N)_k$ Chern Simons gauge group in the presence of a uniform background magnetic field for the $U(1)$ global symmetry of this theory. The magnetic field modifies the Schwinger Dyson equation for the propagator in an interesting way; the product between the self energy and the Greens function is replaced by a Moyal star product. Employing a basis of functions previously used in the study of non-commutative solitons, we are able to exactly solve the Schwinger Dyson equation and so determine the fermion propagator. The propagator has a series of poles (and no other singularities) whose locations yield a spectrum of single particle energies at arbitrary t' Hooft coupling and chemical potential. The usual free fermion Landau levels spectrum is shifted and broadened out; we compute the shifts and widths of these levels at arbitrary t'Hooft coupling. As a check on our results we independently solve for the propagators of the conjecturally dual theory of Chern Simons gauged large $N$ fundamental Wilson Fisher bosons also in a background magnetic field but this time only at zero chemical potential. The spectrum of single particle states of the bosonic theory precisely agrees with those of the fermionic theory under Bose-Fermi duality.

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arXiv2018

Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories

It has been conjectured that Chern-Simons (CS) gauged `regular' bosons in the fundamental representation are `level-rank' dual to CS gauged critical fermions also in the fundamental representation. Generic relevant deformations of these conformal field theories lead to one of two distinct massive phases. In previous work, the large $N$ thermal free energy for the bosonic theory in the unHiggsed phase has been demonstrated to match the corresponding fermionic results under duality. In this note we evaluate the large $N$ thermal free energy of the bosonic theory in the Higgsed phase and demonstrate that our results, again, perfectly match the predictions of duality. Our computation is performed in a unitary gauge by integrating out the physical excitations of the theory - i.e. W bosons - at all orders in the 't Hooft coupling. Our results allow us to construct an exact quantum effective potential for ${\bar ϕ} ϕ$, the lightest gauge invariant scalar operator in the theory. In the zero temperature limit this exact Landau-Ginzburg potential is non-analytic at ${\bar ϕϕ}=0$. The extrema of this effective potential at positive ${\bar ϕ}ϕ$ solve the gap equations in the Higgsed phase while the extrema at negative ${\bar ϕ} ϕ$ solve the gap equations in the unHiggsed phase. Our effective potential is bounded from below only for a certain range of $x_6$ (the parameter that governs sextic interactions of $ϕ$). This observation suggests that the regular boson theory has a stable vacuum only when $x_6$ lies in this range.

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