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A bstract 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.

A bstract 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 = 2 k + 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.

A bstract We consider the linearised graviton in 4 d 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 labels 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 − 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 .

A bstract We show that the determinant of the co-exact p -form on spheres and anti-de Sitter 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 the 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.

A bstract 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 × 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 × 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.

A bstract We study the time dependence of Rényi/entanglement entropies of locally excited states created by fields with integer spins s ≤ 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 2 s + 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 organized in terms of their representations under the SO(2) T × 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 2 s + 1 polynomial is completely determined by the spin.

A bstract 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 〈 T T T 〉 and 〈 jjT 〉 correlation functions which are unique to three space-time dimensions. Let the parameters which determine the 〈 T T T 〉 correlation function be t 4 and α T , where α T is the parity-violating contribution. Similarly let the parameters which determine 〈 jjT 〉 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.

A bstract 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.

A bstract 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.

A bstract 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 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.