Rajesh Gopakumar

A Mellin space approach to the conformal bootstrap

A bstractWe describe in more detail our approach to the conformal bootstrap which uses the Mellin representation of CFTd four point functions and expands them in terms of crossing symmetric combinations of AdSd+1 Witten exchange functions. We consider arbitrary external scalar operators and set up the conditions for consistency with the operator product expansion. Namely, we demand cancellation of spurious powers (of the cross ratios, in position space) which translate into spurious poles in Mellin space. We discuss two contexts in which we can immediately apply this method by imposing the simplest set of constraint equations. The first is the epsilon expansion. We mostly focus on the Wilson-Fisher fixed point as studied in an epsilon expansion about d = 4. We reproduce Feynman diagram results for operator dimensions to O(ϵ3) rather straightforwardly. This approach also yields new analytic predictions for OPE coefficients to the same order which fit nicely with recent numerical estimates for the Ising model (at ϵ = 1). We will also mention some leading order results for scalar theories near three and six dimensions. The second context is a large spin expansion, in any dimension, where we are able to reproduce and go a bit beyond some of the results recently obtained using the (double) light cone expansion. We also have a preliminary discussion about numerical implementation of the above bootstrap scheme in the absence of a small parameter.

String Theory as a Higher Spin Theory

A bstractThe symmetries of string theory on AdS3×S3×T4

Tensionless string spectra on AdS3

{mathrm{AdS}}_3times {mathrm{S}}^3times {mathbb{T}}^4

BPS spectrum on AdS3×S3×S3×S1

at the dual of the symmetric product orbifold point are described by a so-called Higher Spin Square (HSS). We show that the massive string spectrum in this background organises itself in terms of representations of this HSS, just as the matter in a conventional higher spin theory does so in terms of representations of the higher spin algebra. In particular, the entire untwisted sector of the orbifold can be viewed as the Fock space built out of the multiparticle states of a single representation of the HSS, the so-called ‘minimal’ representation. The states in the twisted sector can be described in terms of tensor products of a novel family of representations that are somewhat larger than the minimal one.

BPS spectrum on AdS 3 ×S 3 ×S 3 ×S 1

A bstractWe investigate the behaviour of the bosonic string on AdS3 with H-flux at stringy scales, looking in particular for a ‘tensionless’ limit in which there are massless higher spin gauge fields. We do this by revisiting the physical spectrum of the sl2,ℝk

Stephen Hawking (1942–2018)

mathfrak{s}mathfrak{l}{left(2, mathbb{R}right)}_k