Abstract:We derive the subleading soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. Our results are valid to all orders in perturbation theory when the number of non-compact space-time dimensions is six or more, but only for tree amplitudes for five or less non-compact space-time dimensions due to enhanced contribution to loop amplitudes from the infrared region.

Abstract:We study the SYK model with complex fermions, in the presence of an all-toall q-body interaction, with a non-vanishing chemical potential. We find that, in the large q limit, this model can be solved exactly and the corresponding Lyapunov exponent can be obtained semi-analytically. The resulting Lyapunov exponent is a sensitive function of the chemical potential µ. Even when the coupling J, which corresponds to the disorder averaged values of the all to all fermion interaction, is large, values of µ which are exponentially small compared to J lead to suppression of the Lyapunov exponent.

Although BMPV black holes in flat space and in Taub-NUT space have identical near-horizon geometries, they have different indices from the microscopic analysis. For K3 compactification of type IIB theory, Sen et al. in a series of papers identified that the key to resolving this puzzle is the black hole hair modes: smooth, normalisable, bosonic and fermionic degrees of freedom living outside the horizon. In this paper, we extend their study to N = 4 CHL orbifold models. For these models, the puzzle is more challenging due to the presence of the twisted sectors. We identify hair modes in the untwisted as well as twisted sectors. We show that after removing the contributions of the hair modes from the microscopic partition functions, the 4d and 5d horizon partition functions agree. Special care is taken to present details on the smoothness analysis of hair modes for rotating black holes, thereby filling an essential gap in the literature.

In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY formula.

We study $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ deformations of chiral bosons using the formalism due to Sen. For arbitrary numbers of left- and right-chiral bosons, we find that the $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ -deformed Lagrangian can be computed in closed form, giving rise to a novel non-local action in Sen’s formalism. We establish that at the limit of infinite $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ coupling, the equations of motion of deformed theory exhibits chiral decoupling. We then turn to a discussion of $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ -deformed chiral fermions, and point out that the stress tensor of the $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ -deformed free fermion coincides with the undeformed seed theory. We explain this behaviour of the stress tensor by noting that the deformation term in the action is purely topological in nature and closely resembles the fermionic Wess-Zumino term in the Green-Schwarz formalism. In turn, this observation also explains a puzzle in the literature, viz. why the $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ deformation of multiple free fermions truncate at linear order. We conclude by discussing the possibility of an interplay between $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ deformations and bosonisation.