Quantum Fields and Strings

The partition function on the three-sphere of many supersymmetric Chern-Simons-matter theories reduces, by localization, to a matrix model. In this talk I will describe a new method to study these models in the M-theory limit, but at all orders in the 1/N expansion. The method is based on reformulating the matrix model as the partition function of a Fermi gas. This new approach leads to a completely elementary derivation of the N^{3/2} behavior for ABJM theory and other quiver Chern-Simons-matter theories. In addition, the full series of 1/N corrections to the original matrix integral can be simply determined by a next-to-leading calculation in the semiclassical expansion of the quantum gas.

In this talk I will give an overview of localization and some of its applications for QFTs in three dimensions. I will start by reviewing the localization procedure for N=2 supersymmetric gauge theories in three dimensions on S^3. I will then describe some of the applications to field theory dualities and to holography, and the possibility of extracting information about RG fixed points from the localized partition function.

We investigate the use of the embedding formalism and the Mellin transform in the calculation of tree-level conformal correlation functions in $AdS$/CFT. We evaluate 5- and 6-point Mellin amplitudes in $phi^3$ theory and even a 12-pt diagram in $phi^4$ theory, enabling us to conjecture a set of Feynman rules for scalar Mellin amplitudes. We also show how to use the same combination of Mellin transform and embedding formalism for amplitudes involving fields with spin. The complicated tensor structures which usually arise can be written as certain operators acting as projectors on much simpler index structures - essentially the same ones appearing in a flat space amplitude. Using these methods we are able to evaluate a four-point current diagram with current exchange in Yang-Mills theory.

A non-trivial test of the string vs. integrability correspondence is suggested: exact equivalence is established between strings in AdS4 x CP3 and the Gromov-Vieira all-loop integrable chain. To do that, the complete one- and two-magnon sector of each respective theory are calculated. In the single-magnon sector a direct perturbative one-loop calculation proves the validity of the dispersion law coming from the Bethe Ansatz, rather than of the one coming from the semiclassical analysis. In the two-magnon sector the full spectrum of the finite-size corrections has been calculated on the string side by us for the first time, that proves to be identical to the integrable chain spectrum. These results are interpreted by us as a confirmation of the exactness of the conjectured Gromov-Vieira Bethe Ansatz.

Critical theories of gravity are certain higher derivative theories in which parameters are so tuned as to eliminate massive excitations for the spin-2 field. Asymptotically AdS black hole entropy in these theories works out to be zero. We show that such theories arise naturally on the boundary of AdS in the form of counterterms. Such counterterms are derived by demanding cutoff independence of the Euclidean onshell action and black hole entropy. The resummed higher derivative action so obtained can be shown to be critical. Connections with log-CFTs will be discussed. For a specific choice of parameters, these theories turn out to be non-dynamical.

Taking String Theory as a ``theoretical laboratory'', I will present handy expressions for bosonic and fermionic (SUSY) higher-spin Noether currents. I will also describe a class of non-local higher-spin Lagrangian couplings that are generically required by the Noether procedure starting from four-points. The construction clarifies the origin of old problems for these systems and links String Theory to some aspects of Field Theory that go beyond its conventional low energy limit. I will finally discuss how the extension of these results to (A)dS brings about the emergence of minimal-like couplings from higher-derivative ones.

In this talk I will provide evidence supporting the Dolan/Nirschl/Osborn conjecture for the precise form of the amplitude of four-point functions of 1/2-BPS operators in N=4 SYM theory at strong coupling and in the large N limit. I will also discuss the methods that allowed the evaluation of amplitudes involving operators of arbitrary conformal dimension.

In this talk, I will present a first principle construction of a holographic dual for gauged matrix models. The dual theory is a closed string field theory coupled with an emergent two-form gauge field defined in one higher dimensional space. The bulk space with an extra dimension emerges as a well defined classical background only when the two-form gauge field is in the deconfinement phase. Based on this, it is shown that critical phases that admit holographic descriptions form a novel universality class with a non-trivial quantum order.

Sound waves with long-distance propagation are both a consequence of hydrodynamics, and a danger to hydrodynamics' very existence, as they violate the assumption of local equilibration. In the talk, I will discuss what the thermally excited sound and shear waves do to viscosity. In 2+1 dimensions, the shear viscosity and the diffusion constant cease being independent transport coefficients. In 3+1 dimensions, the fluctuations render the second-order hydrodynamics invalid.

I will discuss three ways in which (the string landscape and) eternal inflation is fun: (1) because it motivates revisiting some beautiful, classic calculations; (2) because its global description requires asking novel questions with possible broad ramifications; and (3) because it leads to experimental predictions.