The Conformal Bootstrap at Finite Temperature

We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a "thermal inversion formula" whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical $O(N)$ model at leading order in $1/N$. Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.Comment: 59 pages plus appendices, 14 figures. v2: added refs, minor correction

Fermions at finite density in the nonrelativistic gauge/gravity duality

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 49-52).The AdS/CFT correspondence has provided a new tool to investigate strongly correlated systems in condensed matter physics. This thesis presents the computation of retarded fermion Green functions at finite density and zero temperature in the nonrelativistic gauge/gravity duality. We find evidence of Fermi surfaces and investigate their properties. We show that the near-horizon scaling dimension, an important quantity that controls the low-energy excitations of the theory, depends on the momentum along the "extra" direction in nonrelativistic gauge/gravity duality.by Raghu Mahajan.S.B