arXiv subjects

Vipul Kumar

Publications and source records attributed to Vipul Kumar.

5 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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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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arXiv2023

Regge constraints on local four-point scattering amplitudes of massive particles with spin

In this work, we classify all the possible local four-point couplings relevant for tree-level flat space $2 \rightarrow 2$ scattering of external massive particles of spin one and spin two which do not grow faster than $s^2$ at large $s$ and fixed t. This kinematic constraint on local growth of tree-level S-matrices is known as Classical Regge Growth criteria or CRG. We first construct the spin one and spin two tree-level contact S-matrices as modules of polarisation tensors and momenta over the ring of polynomials generated by Mandelstam invariants. We then consider a general scattering process where the external scattering particles are of different masses but of same spin and constrain this space to obtain a finite number of CRG allowed local Lagrangians. Our concrete results are primarily for $D\geq 8$ but the process outlined is easily generalised to lower dimensions to include low dimensional parity violating structures. The space of CRG allowed structures reduces when we specialise to identical scattering and restrict to parity even couplings in $D=4$. We show that tree-level scattering amplitudes involving exchange diagrams and contact terms in de Rham-Gabadadze-Tolley massive gravity (dRGT) violate CRG unless the parameters of the theory take special values. The CRG allowed S-matrices, in the context of large $N$ conformal field theories (CFTs), can also be interpreted as bulk $AdS$ counterterms consistent with Chaos bound. Our classified structures therefore can be thought of as ambiguities arising in the context of conformal field theory inversion formula for four point functions of unconserved spin one and spin two operators in large $N$ CFTs.

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arXiv2020

Wigner functions in quantum mechanics with a minimum length scale arising from generalized uncertainty principle

In this paper we generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale arising due to the application of a generalized uncertainty principle (GUP). We present the phase space formulation of such theories following GUP and show that the Weyl transform and the Wigner function does satisfy some of their known properties in standard quantum mechanics. We utilise the generalized Wigner function to calculate the phase space average of the Hamiltonian of a quantum harmonic oscillator satisfying deformed Heisenberg algebra. It is also shown that averages of certain quantum mechanical operators in such theories may restrict the value of the deformation parameter specifying the degree of deformation of Heisenberg algebra. All the results presented are for pure states. The results can be generalized for mixed states.

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