Subham Dutta Chowdhury | Indian Institute of Science (original) (raw)

Uploads

Papers by Subham Dutta Chowdhury

We explicitly construct every kinematically allowed three particle graviton-graviton-P and photon... more We explicitly construct every kinematically allowed three particle graviton-graviton-P and photonphoton-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 veries one of the assumptions made in the recent preprint 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.

JHEP, 2019

We study the Regge trajectories of the Mellin amplitudes of the 0−, 1− and 2− magnon correlators ... more We study the Regge trajectories of the Mellin amplitudes of the 0−, 1− and 2− magnon correlators of the Fishnet theory. Since fishnet theory is both integrable and conformal, the correlation functions are known exactly. We find that while for 0 and 1 magnon correlators, the Regge poles can be exactly determined as a function of coupling, 2-magnon correlators can only be dealt with perturbatively. We evaluate the resulting Mellin amplitudes at weak coupling, while for strong coupling we do an order of magnitude calculation.

We study the crossing equations in d=3 for the four point function of two U(1) currents and two s... more 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.

We study holographic shear sum rules in Einstein gravity with curvature squared corrections. Sum ... more We study holographic shear sum rules in Einstein gravity with curvature squared corrections. Sum rules relate weighted integral over spectral densities of retarded correlators in the shear channel to the one point functions of the CFTs. The proportionality constant can be written in terms of the data of three point functions of the stress tensors of the CFT (t 2 and t 4). For CFTs dual to two derivative Einstein gravity, this proportionality constant is just d 2(d+1). This has been verified by a direct holographic computation of the retarded correlator for Einstein gravity in AdS d+1 black hole background. We compute corrections to the holographic shear sum rule in presence of higher derivative corrections to the Einstein-Hilbert action. We find agreement between the sum rule obtained from a general CFT analysis and holo-graphic computation for Gauss Bonnet theories in AdS 5 black hole background. We then generalize the sum rule for arbitrary curvature squared corrections to Einstein-Hilbert action in d ≥ 4. Evaluating the parameters t 2 and t 4 for the possible dual CFT in presence of such curvature corrections, we find an agreement with the general field theory derivation to leading order in coupling constants of the higher derivative terms.

We derive constraints on three-point functions involving the stress ten-sor, T , and a conserved ... more We derive constraints on three-point functions involving the stress ten-sor, 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 Mal-dacena. 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.

We derive spectral sum rules in the shear channel for conformal field theories at finite temperat... more We derive spectral sum rules in the shear channel for conformal field theories at finite temperature in general d ≥ 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 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.

We investigate the constraints imposed by global gravitational anomalies on parity odd induced tr... more 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 Gaum\'{e} and Witten. The result for the transport coefficient agrees with that obtained using matching of global anomalies.

We evaluate the contribution of chiral fermions in d=2,4,6d=2, 4, 6d=2,4,6, chiral bosons, a chiral gravitin... more We evaluate the contribution of chiral fermions in d=2,4,6d=2, 4, 6d=2,4,6, chiral bosons, a chiral gravitino like theory in d=2d=2d=2 and chiral gravitinos in d=6d=6d=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=2d=2d=2 and chiral gravitinos in d=6d=6d=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.

Drafts by Subham Dutta Chowdhury

We study the space of all kinematically allowed four photon and four graviton S-matrices, polynom... more 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 ≤ 6. For D ≥ 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 ≤ 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 ≤ 6, even when the exchanged particles have low spin.

JHEP, 2019