arXiv subjects

Justin R. David

Publications and source records attributed to Justin R. David.

At least 37 records · Page 2Linked to original sources

arXiv2019

Renyi divergences from Euclidean quenches

We study the generalisation of relative entropy, the Renyi divergence $D_α ( ρ||ρ_β) $ in 2$d$ CFTs between an excited state density matrix $ρ$, created by deforming the Hamiltonian, and the thermal density matrix $ρ_β$. Using the path integral representation of this quantity as a Euclidean quench, we obtain the leading contribution to the Renyi divergence for deformations by scalar primaries and by conserved holomorphic currents in conformal perturbation theory. Furthermore, we calculate the leading contribution to the Renyi divergence when the conserved current perturbations have inhomogeneous spatial profiles which are versions of the sine-square deformation (SSD). The dependence on the Renyi parameter ($α$) of the leading contribution have a universal form for these inhomogeneous deformations and it is identical to that seen in the Renyi divergence of the simple harmonic oscillator perturbed by a linear potential. Our study of these Renyi divergences shows that the family of second laws of thermodynamics, which are equivalent to the monotonicity of Renyi divergences, do indeed provide stronger constraints for allowed transitions compared to the traditional second law.

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arXiv2019

Chaos bound in Bershadsky-Polyakov theory

We consider two dimensional conformal field theory (CFT) with large central charge c in an excited state obtained by the insertion of an operator Φwith large dimension Δ_Φ~ O(c) at spatial infinities in the thermal state. We argue that correlation functions of light operators in such a state can be viewed as thermal correlators with a rescaled effective temperature. The effective temperature controls the growth of out-of-time order (OTO) correlators and results in a violation of the universal upper bound on the associated Lyapunov exponent when Δ_Φ<0 and the CFT is nonunitary. We present a specific realization of this situation in the holographic Chern-Simons formulation of a CFT with {W}^{(2)}_3 symmetry also known as the Bershadsky-Polyakov algebra. We examine the precise correspondence between the semiclassical (large-c) representations of this algebra and the Chern-Simons formulation, and infer that the holographic CFT possesses a discretuum of degenerate ground states with negative conformal dimension Δ_Φ=- c/8. Using the Wilson line prescription to compute entanglement entropy and OTO correlators in the holographic CFT undergoing a local quench, we find the Lyapunov exponent λ_L = 4π/ β, violating the universal chaos bound.

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arXiv2019

Boundary conditions and localization on AdS: Part 2 General analysis

We develop the method of Green's function to evaluate the one loop determinants that arise in localization of supersymmetric field theories on $AdS$ spaces. The theories we study have at least ${\cal N}=2$ supersymmetry and normalisable boundary conditions are consistent with supersymmetry. We then show that under general assumptions the variation of the one loop determinant with respect to the localizing background reduces to a total derivative. Therefore it receives contributions only from the origin of $AdS$ and from asymptotic infinity. From expanding both the Greens function and the quadratic operators at the origin of $AdS$ and asymptotic infinity, we show that the variation of the one loop determinant is proportional to an integer. Furthermore, we show that this integer is an index of a first order differential operator. We demonstrate that these assumptions are valid for Chern-Simons theories coupled to chiral multiplets on $AdS_2\times S^1$. Finally we use our results to show that $U(N_c)$ Chern-Simons theory at level $k$ coupled to $N_f$ chiral multiplets and $N_f$ anti-chiral multiplets in the fundamental obeys level-rank duality on $AdS_2\times S^1$.

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arXiv2019

Properties of dyons in ${\cal N}=4$ theories at small charges

We study three properties of $1/4$ BPS dyons at small charges in string compactifications which preserve ${\cal N}=4$ supersymmetry. We evaluate the non-trivial constant present in the one loop statistical entropy for ${\cal N}=4$ compactifications of type IIB theory on $K3\times T^2$ orbifolded by an order $\mathbb{Z}_N$ freely acting orbifold $g'$ including all CHL compactifications. This constant is trivial for the un-orbifolded model but we show that it contributes crucially to the entropy of low charge dyons in all the orbifold models. We then show that the meromorphic Jacobi form which captures the degeneracy of $1/4$ BPS states for the first two non-trivial magnetic charges can be decomposed into an Appell-Lerch sum and a mock Jacobi form transforming under $Γ_0(N)$. This generalizes the earlier observation of Dabholkar-Murthy-Zagier to the orbifold models. Finally we study the sign of the Fourier coefficients of the inverse Siegel modular form which counts the index of $1/4$ BPS dyons in ${\cal N}=4$ models obtained by freely acting $\mathbb{Z}_2$ and $\mathbb{Z}_3$ orbifolds of type II theory compactified on $T^6$. We show that sign of the index for sufficiently low charges and ensuring that it counts single centered black holes, violates the positivity conjecture of Sen which indicates that these states posses non-trivial hair.

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arXiv2019

Bootstrap and collider physics of parity violating conformal field theories in $d=3$

We study the crossing equations in $d=3$ for the four point function of two $U(1)$ currents and two scalars including the presence of a parity violating term for the $s$-channel stress tensor exchange. We show the existence of a new tower of double trace operators in the $t$-channel whose presence is necessary for the crossing equation to be satisfied and determine the corresponding large spin parity violating OPE coefficients. Contrary to the parity even situation, we find that the parity odd $s$-channel light cone stress tensor block do not have logarithmic singularities. This implies that the parity odd term does not contribute to anomalous dimensions in the crossed channel at this order in light cone expansion. We then study the constraints imposed by reflection positivity and crossing symmetry on such a four point function. We reproduce the previously known parity odd collider bounds through this analysis. The contribution of the parity violating term in the collider bound results from a square root branch cut present in the light cone block as opposed to a logarithmic cut in the parity even case, together with the application of the Cauchy-Schwarz inequality.

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arXiv2018

Boundary Conditions and Localization on AdS: Part 1

We study the role of boundary conditions on the one loop partition function of ${\cal N}=2$ chiral multiplet of R-charge $Δ$ on $AdS_2\times S^1$. The chiral multiplet is coupled to a background vector multiplet which preserves supersymmetry. We implement normalizable boundary conditions in $AdS_2$ and develop the Green's function method to obtain the one loop determinant. We evaluate the one loop determinant for two different actions: the standard action and the $Q$-exact deformed positive definite action used for localization. We show that if there exists an integer $n$ in the interval $D: ( \frac{Δ-1}{2L}, \fracΔ{2L} )$, where $L$ being the ratio of radius of $AdS_2$ to that of $S^1$, then the one loop determinants obtained for the two actions differ. It is in this situation that fields which obey normalizable boundary conditions do not obey supersymmetric boundary conditions. However if there are no integers in $D$, then fields which obey normalizable boundary conditions also obey supersymmetric boundary conditions and the one loop determinants of the two actions precisely agree. We also show that it is only in the latter situation that the one loop determinant obtained by evaluating the index of the $D_{10}$ operator associated with the localizing action agrees with the one loop determinant obtained using Green's function method.

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arXiv2018

Gravitational couplings in ${\cal N}=2$ string compactifications and Mathieu Moonshine

We evaluate the low energy gravitational couplings, $F_g$ in the heterotic $E_8\times E_8$ string theory compactified on orbifolds of $K3\times T^2$ by $g'$ which acts as a $\mathbb{Z}_N$ automorphisim on $K3$ together with a $1/N$ shift along $T^2$. The orbifold $g'$ corresponds to the conjugacy classes of the Mathieu group $M_{24}$. The holomorphic piece of $F_g$ is given in terms of a polylogarithim with index $3-2g$ and predicts the Gopakumar-Vafa invariants in the corresponding dual type II Calabi-Yau compactifications. We show that low lying Gopakumar-Vafa invariants for each of these compactifications including the twisted sectors are integers. We observe that the conifold singularity for all these compactifications occurs only when states in the twisted sectors become massless and the strength of the singularity is determined by the genus zero Gopakumar-Vafa invariant at this point in the moduli space.

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arXiv2017

Local quenches and quantum chaos from higher spin perturbations

We study local quenches in 1+1 dimensional conformal field theories at large-c by operators carrying higher spin charge. Viewing such states as solutions in Chern-Simons theory, representing infalling massive particles with spin-three charge in the BTZ background, we use the Wilson line prescription to compute the single-interval entanglement entropy (EE) and scrambling time following the quench. We find that the change in EE is finite (and real) only if the spin-three charge q is bounded by the energy of the perturbation E, as |q|/c < E^2/c^2. We show that the Wilson line/EE correlator deep in the quenched regime and its expansion for small quench widths overlaps with the Regge limit for chaos of the out-of-time-ordered correlator. We further find that the scrambling time for the two-sided mutual information between two intervals in the thermofield double state increases with increasing spin-three charge, diverging when the bound is saturated. For larger values of the charge, the scrambling time is shorter than for pure gravity and controlled by the spin-three Lyapunov exponent 4π/β. In a CFT with higher spin chemical potential, dual to a higher spin black hole, we find that the chemical potential must be bounded to ensure that the mutual information is a concave function of time and entanglement speed is less than the speed of light. In this case, a quench with zero higher spin charge yields the same Lyapunov exponent as pure Einstein gravity.

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arXiv2017

Constraints on parity violating conformal field theories in $d=3$

We derive constraints on three-point functions involving the stress tensor, $T$, and a conserved $U(1)$ current, $j$, in 2+1 dimensional conformal field theories that violate parity, using conformal collider bounds introduced by Hofman and Maldacena. Conformal invariance allows parity-odd tensor-structures for the $\langle T T T \rangle$ and $ \langle j j T \rangle$ correlation functions which are unique to three space-time dimensions. Let the parameters which determine the $\langle T T T \rangle$ correlation function be $t_4$ and $α_T$ , where $α_T$ is the parity-violating contribution. Similarly let the parameters which determine $ \langle j j T \rangle$ correlation function be $a_2$, and $α_J$ , where $α_J$ is the parity-violating contribution. We show that the parameters $(t_4, α_T)$ and $(a_2, α_J)$ are bounded to lie inside a disc at the origin of the $t_4$ - $α_T$ plane and the $a_2$ - $α_J$ plane respectively. We then show that large $N$ Chern-Simons theories coupled to a fundamental fermion/boson lie on the circle which bounds these discs. The `t Hooft coupling determines the location of these theories on the boundary circles.

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arXiv2017

Spectral sum rules for conformal field theories in arbitrary dimensions

We derive spectral sum rules in the shear channel for conformal field theories at finite temperature in general $d\geq 3$ dimensions. The sum rules result from the OPE of the stress tensor at high frequency as well as the hydrodynamic behaviour of the theory at low frequencies. The sum rule states that a weighted integral of the spectral density over frequencies is proportional to the energy density of the theory. We show that the proportionality constant can be written in terms the Hofman-Maldacena variables $t_2, t_4$ which determine the three point function of the stress tensor. For theories which admit a two derivative gravity dual this proportionality constant is given by $\frac{d}{2(d+1)}$. We then use causality constraints and obtain bounds on the sum rule which are valid in any conformal field theory. Finally we demonstrate that the high frequency behaviour of the spectral function in the vector and the tensor channel are also determined by the Hofman-Maldacena variables.

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arXiv2017

Dyon degeneracies from Mathieu moonshine

We construct the Siegel modular forms associated with the theta lift of twisted elliptic genera of $K3$ orbifolded with $g'$ corresponding to the conjugacy classes of the Mathieu group $M_{24}$. We complete the construction for all the classes which belong to $M_{23} \subset M_{24}$ and two other classes outside the subgroup $M_{23}$. For this purpose we provide the explicit expressions for all the twisted elliptic genera in all the sectors of these classes. We show that the Siegel modular forms satisfy the required properties for them to be generating functions of $1/4$ BPS dyons of type II string theories compactified on $K3\times T^2$ and orbifolded by $g'$ which acts as a $\mathbb{Z}_N$ automorphism on $K3$ together with a $1/N$ shift on a circle of $T^2$. In particular the inverse of these Siegel modular forms admit a Fourier expansion with integer coefficients together with the right sign as predicted from black hole physics. Our analysis completes the construction of the partition function for dyons as well as the twisted elliptic genera for all the $7$ CHL compactifications.

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arXiv2016

${\cal N}=2$ heterotic string compactifications on orbifolds of $K3\times T^2$

We study ${\cal N}=2$ compactifications of $E_8\times E_8$ heterotic string theory on orbifolds of $K3 \times T^2$ by $g'$ which acts as an $\mathbb{Z}_N$ automorphism of $K3$ together with a$1/N$ shift on a circle of $T^2$. The orbifold action $g'$ corresponds to the $26$ conjugacy classes of the Mathieu group $M_{24}$. We show that for the standard embedding the new supersymmetric index for these compactifications can always be decomposed into the elliptic genus of $K3$ twisted by $g'$. The difference in one-loop corrections to the gauge couplings are captured by automorphic forms obtained by the theta lifts of the elliptic genus of $K3$ twisted by $g'$. We work out in detail the case for which $g'$ belongs to the equivalence class $2B$. We then investigate all the non-standard embeddings for$K3$ realized as a $T^4/\mathbb{Z}_ν$ orbifold with $ν= 2, 4$ and $g'$ the $2A$ involution. We show that for non-standard embeddings the new supersymmetric index as well as the difference in one-loop corrections to the gauge couplings are completely characterized by the instanton numbers of the embeddings together with the difference in number of hypermultiplets and vector multiplets in the spectrum.

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arXiv2016

Localization on $AdS_2\times S^1$

Conformal symmetry relates the metric on $AdS_2 \times S^{1}$ to that of $S^3$. This implies that under a suitable choice of boundary conditions for fields on $AdS_2$ the partition function of conformal field theories on these spaces must agree which makes $AdS_2 \times S^{1}$ a good testing ground to study localization on non-compact spaces. We study supersymmetry on $AdS_2\times S^1$ and determine the localizing Lagrangian for ${\cal N}=2$ supersymmetric Chern-Simons theory on $AdS_2\times S^1$. We evaluate the partition function of ${\cal N}=2$ supersymmetric Chern-Simons theory on $AdS_2 \times S^1$ using localization, where the radius of $S^1$ is $q$ times that of $AdS_2$. With boundary conditions on $AdS_2\times S^1$ which ensure that all the physical fields are normalizable and lie in the space of square integrable wave functions in $AdS_2$, the result for the partition function precisely agrees with that of the theory on the $q$-fold covering of $S^3$.

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arXiv2016

Universal corrections to entanglement entropy of local quantum quenches

We study the time evolution of single interval Renyi and entanglement entropies following local quantum quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width, ε. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Renyi and entanglement entropies at order ε^2 is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the ε^2 correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We then consider CFTs admitting a higher spin symmetry and turn on a higher spin chemical potential μ. We calculate the time dependence of the order ε^2 correction to the entanglement entropy for small μ, and show that the contribution at order μ^2 is universal. We verify our arguments against exact results for minimal models and the free fermion theory.

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arXiv2016

Global gravitational anomalies and transport

We investigate the constraints imposed by global gravitational anomalies on parity odd induced transport coefficients in even dimensions for theories with chiral fermions, gravitinos and self dual tensors. The $η$-invariant for the large diffeomorphism corresponding to the $T$ transformation on a torus constraints the coefficients in the thermal effective action up to mod 2. We show that the result obtained for the parity odd transport for gravitinos using global anomaly matching is consistent with the direct perturbative calculation. In $d=6$ we see that the second Pontryagin class in the anomaly polynomial does not contribute to the $η$-invariant which provides a topological explanation of this observation in the `replacement rule'. We then perform a direct perturbative calculation for the contribution of the self dual tensor in $d=6$ to the parity odd transport coefficient using the Feynman rules proposed by Gaumé and Witten. The result for the transport coefficient agrees with that obtained using matching of global anomalies.

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arXiv2015

Heterotic string on the CHL orbifold of K3

We study ${\cal N}=2$ compactifications of heterotic string theory on the CHL orbifold $(K3\times T^2)/\mathbb{Z}_N$ with $N= 2, 3, 5, 7$. $\mathbb{Z}_N$ acts as an involution on $K3$ together with a shift of $1/N$ along one of the circles of $T^2$. These compactifications generalize the example of the heterotic string on $K3\times T^2$ studied in the context of dualities in ${\cal N}=2$ string theories. We evaluate the new supersymmetric index for these theories and show that their expansion can written in terms of the McKay-Thompson series associated with the $\mathbb{Z}_N$ involution embedded in the Mathieu group $M_{24}$. We then evaluate the difference in one-loop threshold corrections to the non-Abelian gauge couplings with Wilson lines and show that their moduli dependence is captured by Siegel modular forms related to dyon partition functions of ${\cal N}=4$ string theories.

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arXiv2015

Anomalous transport at weak coupling

We evaluate the contribution of chiral fermions in $d=2, 4, 6$, chiral bosons, a chiral gravitino like theory in $d=2$ and chiral gravitinos in $d=6$ to all the leading parity odd transport coefficients at one loop. This is done by using finite temperature field theory to evaluate the relevant Kubo formulae. For chiral fermions and chiral bosons the relation between the parity odd transport coefficient and the microscopic anomalies including gravitational anomalies agree with that found by using the general methods of hydrodynamics and the argument involving the consistency of the Euclidean vacuum. For the gravitino like theory in $d=2$ and chiral gravitinos in $d=6$, we show that relation between the pure gravitational anomaly and parity odd transport breaks down. From the perturbative calculation we clearly identify the terms that contribute to the anomaly polynomial, but not to the transport coefficient for gravitinos. We also develop a simple method for evaluating the angular integrals in the one loop diagrams involved in the Kubo formulae. Finally we show that charge diffusion mode of an ideal 2 dimensional Weyl gas in the presence of a finite chemical potential acquires a speed, which is equal to half the speed of light.

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arXiv2015

Thermalization of Green functions and quasinormal modes

We develop a new method to study the thermalization of time dependent retarded Green function in conformal field theories holographically dual to thin shell AdS Vaidya space times. The method relies on using the information of all time derivatives of the Green function at the shell and then evolving it for later times. The time derivatives of the Green function at the shell is given in terms of a recursion formula. Using this method we obtain analytic results for short time thermalization of the Green function. We show that the late time behaviour of the Green function is determined by the first quasinormal mode. We then implement the method numerically. As applications of this method we study the thermalization of the retarded time dependent Green function corresponding to a minimally coupled scalar in the AdS3 and AdS5 thin Vaidya shells. We see that as expected the late time behaviour is determined by the first quasinormal mode. We apply the method to study the late time behaviour of the shear vector mode in AdS5 Vaidya shell. At small momentum the corresponding time dependent Green function is expected to relax to equilibrium by the shear hydrodynamic mode. Using this we obtain the universal ratio of the shear viscosity to entropy density from a time dependent process.

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