arXiv subjects

Justin R. David

Publications and source records attributed to Justin R. David.

At least 19 recordsLinked to original sources

arXiv2026

The large $N$ vector model with angular velocity

We study the free energy of a critical vector model at large $N$ on $S^{1}\times S^{2}$ with an angular velocity $\hat\mu$ without the singlet constraint. We study the model for which the large $N$ dynamics is controlled by the uniform saddle point of the auxiliary field arising in the Hubbard-Stratanovich transformation. The leading high-temperature behaviour is determined analytically both as an expansion about $\hat\mu r=0$ and $\hat\mu^{2}r^{2}=1$ where $r$ is the radius of the sphere. We supplement the analytic results with a numerical analysis that agrees with both the analytical expansions in their respective regimes and smoothly interpolates between them. The leading high-temperature contribution to the free energy develops a pole at $\hat\mu^{2}r^{2}=1$, in agreement with expectations from the thermal effective field theory. Its residue coincides with that of the massless free theory. Sub-leading terms, however, exhibit non-analytic dependence on the angular velocity and distinguish the critical fixed-point result from the free theory answer. The residue at the pole can also be obtained by placing the model on the pp-wave geometry. We show that the residue agrees with that obtained from the direct computation. The free energy of the model connects the non-trivial fixed point of the $O(N)$ model at $\hat\mu r=0$ to its free fixed point at $\hat\mu^2r^2=1$.

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arXiv2026

Holographic Local Operator Quenches with Conserved Momentum and Spin

We investigate the holographic dictionary relating point particles carrying longitudinal momentum or angular momentum in asymptotically AdS$_3$ spacetimes to suitably regulated, time-evolved states created by local primary operators in the dual two-dimensional conformal field theory (2D CFT). We find that asymmetric left/right Euclidean smearing of local operators produces states carrying momentum, and the corresponding bulk excitation is a particle with conserved momentum. We compute the energy density and entanglement entropy in these states and in their dual back-reacted geometries, finding exact agreement between the CFT and gravity descriptions. We further extend this correspondence to particles with intrinsic spin, whose CFT duals are primary operators with unequal holomorphic and anti-holomorphic scaling dimensions. We again find a precise match between CFT and holographic calculations of energy densities and entanglement entropies. Finally, we explore applications of these setups beyond holography by deriving the evolution of R\'enyi entropies in 2D rational CFTs and introducing a new class of local quantum quench protocols with conserved longitudinal or angular momentum.

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arXiv2026

Light-like retarded correlators and the horizon

We show that retarded correlators in conformal field theories of scalar primary operators evaluated at finite temperature using $AdS/CFT$ scale anomalously at large light like momenta. The anomalous scaling depends on the curvature of the horizon. Setting the momenta equal to the frequency $\omega$, the retarded correlator for black holes with planar horizons scales as $\omega^{\frac{2}{d+2} (2\Delta - d) }$ as opposed to the scaling behaviour of $\omega^{2\Delta - d}$ expected by dimensional analysis at generic fixed momenta and large frequencies. $\Delta$ is the dimension of the primary and $d$, the number of space-time dimensions. For black holes with spherical and hyperbolic horizons when the frequency squared equals the Casimir along the horizon, the retarded correlator scales as $\omega^{\frac{2\Delta -d}{2} }$. We establish this using exact results in $d=2$, and a numerical analysis of the Heun equation for the $AdS_5$ planar black hole and finally using the WKB approximation in general $d$. The exact result for black holes with hyperbolic horizon as well as the analysis at large $d$ provides additional checks for the anomalous scaling behaviour. Finally we evaluate the anomalous scaling exponent for the stress tensor correlator in all its 3 channels.

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arXiv2026

Circular strings, magnons, plane waves and local quenches in BTZ

We show that string theory on the geometry $BTZ\times S^3\times M$ supported with either Neveu-Schwarz flux or Ramond flux admits states which obey identical dispersion relations to those of classical solutions like circular strings, giant magnons, or plane wave excitations in the geometry $ AdS_3 \times S^3 \times M$. Here, $M$ can be $T^4$, $K3$, or $S^3\times S^1$. This is made possible by the map, which takes the particle at the origin of $AdS_3$ with angular momentum along one of the angles of $S_3$ to a particle falling into the BTZ horizon. We use this map to construct circular strings, magnons, as well as plane waves in the BTZ geometry. We show that the $SL(2, R)$ charges of these states on $AdS_3$ and that of the corresponding states in the BTZ geometry are related by a boost. The dual description of these states in the BTZ geometry are local quenches in the thermal CFT. These quenches carry energy density, $R$-charges, non-trivial expectation value of the marginal operator dual to the dilaton and move on the light cone in CFT. In general, the left and the right moving quenches are not symmetric.

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arXiv2025

Precision tests of bulk entanglement: $AdS_3$ vectors

We consider single-particle excitations of the massive Chern-Simons field of mass $M$ in $AdS_3$ and evaluate their contribution at the first sub-leading order in $G_N$ to the entanglement entropy across the Ryu-Takayanagi surface. Quantizing the Chern-Simons field in $AdS_3$, we evaluate the corrections to the holographic entanglement entropy using the Faulkner-Lewkowycz-Maldacena formula. The massive Chern-Simons field also obeys the equations of motion of a massive vector in $AdS_3$. The lowest-energy single-particle excitation of this field is dual to the primary operator of conformal dimension $M+1$ with spin one in the dual CFT; all other single-particle excitations are dual to its global descendants. We compare the entanglement entropy result from the FLM formula to the single-interval entanglement entropy in large-charge holographic CFT obtained using the replica trick for the primary and its tower of holomorphic descendants. The two results agree precisely in the leading and sub-leading terms of the short interval expansion. We evaluate the contribution of the edge mode to the vacuum-subtracted entanglement and show that it vanishes, which is crucial for the FLM formula to agree with the CFT result. On taking the massless limit, the result coincides with the contribution of a $U(1)$ current to the single interval entanglement entropy. This is surprising since an earlier calculation in the literature reproduced the CFT result entirely from the edge $U(1)$ degrees of freedom on the RT surface.

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arXiv2025

High to low temperature: $O(N)$ model at large $N$

We study the $O(N)$ vector model for scalars with quartic interaction at large $N$ on $S^1\times S^2$ without the singlet constraint. The non-trivial fixed point of the model is described by a thermal mass satisfying the gap equation at large $N$. We obtain the free energy and the energy density for the model as a series at low temperature in units of the radius of the sphere. We show these results agree with the Borel-Pad\'{e} extrapolations of the high temperature expansions of the free energy and energy density obtained in our previous work. This agreement validates both the expansions and demonstrates that low temperature expansions obtained here correspond to the same solution of the gap equation studied earlier at high temperature. We obtain the ratio of the free energy of the theory at the non-trivial fixed point to that of the Gaussian theory at all values of temperature. This ratio begins at $4/5$ when the temperature is infinity, decreases to a minimum value of $0.760753$, then increases and approaches unity as the temperature is decreased.

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arXiv2024

The large $N$ vector model on $S^1\times S^2$

We develop a method to evaluate the partition function and energy density of a massive scalar on a 2-sphere of radius $r$ and at finite temperature $\beta$ as power series in $\frac{\beta}{r}$. Each term in the power series can be written in terms of polylogarithms. We use this result to obtain the gap equation for the large $N$, critical $O(N)$ model with a quartic interaction on $S^1\times S^2$ in the large radius expansion. Solving the gap equation perturbatively we obtain the leading finite size corrections to the expectation value of stress tensor for the $O(N)$ vector model on $S^1\times S^2$. Applying the Euclidean inversion formula on the perturbative expansion of the thermal two point function we obtain the finite size corrections to the expectation value of the higher spin currents of the critical $O(N)$ model. Finally we show that these finite size corrections of higher spin currents tend to that of the free theory at large spin as seen earlier for the model on $S^1\times R^2$.

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arXiv2024

One point functions in large $N$ vector models at finite chemical potential

We evaluate the thermal one point function of higher spin currents in the critical model of $U(N)$ complex scalars interacting with a quartic potential and the $U(N)$ Gross-Neveu model of Dirac fermions at large $N$ and strong coupling using the Euclidean inversion formula. These models are considered in odd space time dimensions $d$ and held at finite temperature and finite real chemical potential $\mu$ measured in units of the temperature. We show that these one point functions simplify both at large spin and large $d$. At large spin, the one point functions behave as though the theory is free, the chemical potential appears through a simple pre-factor which is either $\cosh\mu$ or $\sinh\mu$ depending on whether the spin is even or odd. At large $d$, but at finite spin and chemical potential, the 1-point functions are suppressed exponentially in $d$ compared to the free theory. We study a fixed point of the critical Gross-Neveu model in $d=3$ with 1-point functions exhibiting a branch cut in the chemical potential plane. The critical exponent for the free energy or the pressure at the branch point is $3/2$ which coincides with the mean field exponent of the Lee-Yang edge singularity for repulsive core interactions.

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arXiv2024

Precision tests of bulk entanglement entropy

We consider linear superpositions of single particle excitations in a scalar field theory on $AdS_3$ and evaluate their contribution to the bulk entanglement entropy across the Ryu-Takayanagi surface. We compare the entanglement entropy of these excitations obtained using the Faulkner-Lewkowycz-Maldacena formula to the entanglement entropy of linear superposition of global descendants of a conformal primary in a large $c$ CFT obtained using the replica trick. We show that the closed from expressions for the entanglement entropy in the small interval expansion both in gravity and the CFT precisely agree. The agreement serves as a non-trivial check of the FLM formula for the quantum corrections to holographic entropy which also involves a contribution from the back reacted minimal area. Our checks includes an example in which the state is time dependent and spatially in-homogenous as well another example involving a coherent state with a Bañados geometry as its holographic dual.

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arXiv2023

Thermal one-point functions: CFT's with fermions, large $d$ and large spin

We apply the OPE inversion formula on thermal two-point functions of fermions to obtain thermal one-point function of fermion bi-linears appearing in the corresponding OPE. We primarily focus on the OPE channel which contains the stress tensor of the theory. We apply our formalism to the mean field theory of fermions and verify that the inversion formula reproduces the spectrum as well as their corresponding thermal one-point functions. We then examine the large $N$ critical Gross-Neveu model in $d=2k+1$ dimensions with $k$ even and at finite temperature. We show that stress tensor evaluated from the inversion formula agrees with that evaluated from the partition function at the critical point. We demonstrate the expectation values of 3 different classes of higher spin currents are all related to each other by numerical constants, spin and the thermal mass. We evaluate the ratio of the thermal expectation values of higher spin currents at the critical point to the Gaussian fixed point or the Stefan-Boltzmann result, both for the large $N$ critical $O(N)$ model and the Gross-Neveu model in odd dimensions. This ratio is always less than one and it approaches unity on increasing the spin with the dimension $d$ held fixed. The ratio however approaches zero when the dimension $d$ is increased with the spin held fixed.

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arXiv2023

Discontinuities of free theories on $AdS_2$

The partition functions of free bosons as well as fermions on $AdS_2$ are not smooth as a function of their masses. For free bosons, the partition function on $AdS_2$ is not smooth when the mass saturates the Breitenlohner-Freedman bound. We show that the expectation value of the scalar bilinear on $AdS_2$ exhibits a kink at the BF bound and the change in slope of the expectation value with respect to the mass is proportional to the inverse radius of $AdS_2$. For free fermions, when the mass vanishes the partition function exhibits a kink. We show that expectation value of the fermion bilinear is discontinuous and the jump in the expectation value is proportional to the inverse radius of $AdS_2$. We then show the supersymmetric actions of the chiral multiplet on $AdS_2\times S^1$ and the hypermultiplet on $AdS_2\times S^2$ demonstrate these features. The supersymmetric backgrounds are such that as the ratio of the radius of $AdS_2$ to $S^1$ or $S^2$ is dialled, the partition functions as well as expectation of bilinears are not smooth for each Kaluza-Klein mode on $S^1$ or $S^2$. Our observation is relevant for evaluating one-loop partition function in the near horizon geometry of extremal black holes.

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arXiv2023

Thermal one point functions, large $d$ and interior geometry of black holes

We study thermal one point functions of massive scalars in $AdS_{d+1}$ black holes. These are induced by coupling the scalar to either the Weyl tensor squared or the Gauss-Bonnet term. Grinberg and Maldacena argued that the one point functions sourced by the Weyl tensor exponentiate in the limit of large scalar masses and they contain information of the black hole geometry behind the horizon. We observe that the one point functions behave identically in this limit for either of the couplings mentioned earlier. We show that in an appropriate large $d$ limit, the one point function for the charged black hole in $AdS_{d+1}$ can be obtained exactly. These black holes in general contain an inner horizon. We show that the one point function exponentiates and contains the information of both the proper time between the outer horizon to the inner horizon as well as the proper length from the inner horizon to the singularity. We also show that Gauss-Bonnet coupling induced one point functions in $AdS_{d+1}$ black holes with hyperbolic horizons behave as anticipated by Grinberg-Maldacena. Finally, we study the one point functions in the background of rotating BTZ black holes induced by the cubic coupling of scalars.

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arXiv2022

Entanglement entropy of local gravitational quenches

We study the time dependence of Rényi/entanglement entropies of locally excited states created by fields with integer spins $s \leq 2$ in $4$ dimensions. For spins 0, 1 these states are characterised by localised energy densities of a given width which travel as a spherical wave at the speed of light. For the spin 2 case, in the absence of a local gauge invariant stress tensor, we probe these states with the Kretschmann scalar and show they represent localised curvature densities which travel at the speed of light. We consider the reduced density matrix of the half space with these excitations and develop methods which include a convenient gauge choice to evaluate the time dependence of Rényi/entanglement entropies as these quenches enter the half region. In all cases, the entanglement entropy grows in time and saturates at $\log 2 $. In the limit, the width of these excitations tends to zero, the growth is determined by order $2s+1$ polynomials in the ratio of the distance from the co-dimension-2 entangling surface and time. The polynomials corresponding to quenches created by the fields can be organised in terms of their representations under the $SO(2)_T\times SO(2)_L$ symmetry preserved by the presence of the co-dimension 2 entangling surface. For fields transforming as scalars under this symmetry, the order $2s+1$ polynomial is completely determined by the spin.

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arXiv2022

Entanglement entropy of gravitational edge modes

We consider the linearised graviton in $4d$ Minkowski space and decompose it into tensor spherical harmonics and fix the gauge. The Gauss law of gravity implies that certain radial components of the Riemann tensor of the graviton on the sphere label the superselection sectors for the graviton. We show that among these 6 normal components of the Riemann tensor, 2 are related locally to the algebra of gauge-invariant operators in the sphere. From the two-point function of these components of the Riemann tensor on $S^2$ we compute the logarithmic coefficient of the entanglement entropy of these superselection sectors across a spherical entangling surface. For sectors labelled by each of the two components of the Riemann tensor these coefficients are equal and their total contribution is given by $-\frac{16}{3}$. We observe that this coefficient coincides with that extracted from the edge partition function of the massless spin-2 field on the 4-sphere when written in terms of its Harish-Chandra character. As a preliminary step, we also evaluate the logarithmic coefficient of the entanglement entropy from the superselection sectors labelled by the radial component of the electric field of the $U(1)$ theory in even $d$ dimensions. We show that this agrees with the corresponding coefficient of the edge Harish-Chandra character of the massless spin-1 field on $S^d$.

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arXiv2021

Partition functions of $p$-forms from Harish-Chandra characters

We show that the determinant of the co-exact $p$-form on spheres and anti-deSitter spaces can be written as an integral transform of bulk and edge Harish-Chandra characters. The edge character of a co-exact $p$-form contains characters of anti-symmetric tensors of rank lower to $p$ all the way to the zero-form. Using this result we evaluate the partition function of $p$-forms and demonstrate that they obey known properties under Hodge duality. We show that partition function of conformal forms in even $d+1$ dimensions, on hyperbolic cylinders can be written as integral transforms involving only the bulk characters. This supports earlier observations that entanglement entropy evaluated using partition functions on hyperbolic cylinders do not contain contributions from the edge modes. For conformal coupled scalars we demonstrate that the character integral representation of the free energy on hyperbolic cylinders and branched spheres coincide. Finally we propose a character integral representation for the partition function of $p$-forms on branched spheres.

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arXiv2021

Entanglement in descendants

We study the single interval entanglement and relative entropies of conformal descendants in 2d CFT. Descendants contain non-trivial entanglement, though the entanglement entropy of the canonical primary in the free boson CFT contains no additional entanglement compared to the vacuum, we show that the entanglement entropy of the state created by its level one descendant is non-trivial and is identical to that of the $U(1)$ current in this theory. We determine the first sub-leading corrections to the short interval expansion of the entanglement entropy of descendants in a general CFT from their four point function on the n-sheeted plane. We show that these corrections are determined by multiplying squares of appropriate dressing factors to the corresponding corrections of the primary. Relative entropy between descendants of the same primary is proportional to the square of the difference of their dressing factors. We apply our results to a class of descendants of generalized free fields and descendants of the vacuum and show that their dressing factors are universal.

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arXiv2021

Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, $p$-forms

We show that the entanglement entropy of $D=4$ linearized gravitons across a sphere recently computed by Benedetti and Casini coincides with that obtained using the Kaluza-Klein tower of traceless transverse massive spin-2 fields on $S^1\times AdS_3$. The mass of the constant mode on $S^1$ saturates the Brietenholer-Freedman bound in $AdS_3$. This condition also ensures that the entanglement entropy of higher spins determined from partition functions on the hyperbolic cylinder coincides with their recent conjecture. Starting from the action of the 2-form on $S^1\times AdS_5$ and fixing gauge, we evaluate the entanglement entropy across a sphere as well as the dimensions of the corresponding twist operator. We demonstrate that the conformal dimensions of the corresponding twist operator agrees with that obtained using the expectation value of the stress tensor on the replica cone. For conformal $p$-forms in even dimensions it obeys the expected relations with the coefficients determining the $3$-point function of the stress tensor of these fields.

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arXiv2020

Horizon states and the sign of their index in ${\cal N}=4$ dyons

Classical single centered solutions of $1/4$ BPS dyons in ${\cal N}=4$ theories are usually constructed in duality frames which contain non-trivial hair degrees of freedom localized outside the horizon. These modes are in addition to the fermionic zero modes associated with broken supersymmetry. Identifying and removing the hair from the $1/4$ BPS index allows us to isolate the degrees of freedom associated with the horizon. The spherical symmetry of the horizon then ensures that index of the horizon states has to be positive. We verify that this is indeed the case for the canonical example of dyons in type IIB theory on $K3\times T^2$ and prove this property holds for a class of states. We generalise this observation to all CHL orbifolds, this involves identifying the hair and isolating the horizon degrees of freedom. We then identify the horizon states for $1/4$ BPS dyons in ${\cal N}=4$ models obtained by freely acting ${\mathbb{Z}}_2$ and ${\mathbb{ Z}}_3$ orbifolds of type IIB theory compactified on $T^6$ and observe that the index is again positive for single centred black holes. This observation coupled with the fact the $1/4$ BPS index of single centred solutions without removal of the hair violates positivity indicates that there exists no duality frame in these models without non-trivial hair.

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