Quantum Fields and Strings

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.

I will discuss the geometry of heterotic string compactifications with fluxes. The compactifications on 6 dimensional manifolds which preserve N=1 supersymmetry in 4 dimensions must be complex manifolds with vanishing first Chern class, but which are not in general Kahler (and therefore not Calabi-Yau manifolds) together with a vector bundle on the manifold which must satisfy a complicated differential equation. The flux, which can be viewed as a torsion, is the obstruction to the manifold being Kahler. I will describe how these compactifications are connected to the more traditional compactifications on Calabi-Yau manifolds through geometric transitions like flops and conifold transitions. For instance, one can construct solutions by flopping rational curves in a Calabi-Yau manifold in such a way that the resulting manifold is no longer Kahler. Time permitting, I will discuss open problems, for example the understanding of the the moduli space of heterotic compactifications and the related problem of determining the massless spectrum in the effective 4 dimensional supersymmetric field theory. The study of these compactifications is interesting on its own right both in string theory, in order to understand more generally the degrees of freedom of these theories, and also in mathematics. For instance, the connectedness between the solutions is related to problems in mathematics like the conjecture by Mile Reid that complex manifolds with trivial canonical bundle are all connected through geometric transitions.

For stationary black holes it is universally agreed that entropy is proportional to horizon area. It is not so clear what the relationship is for dynamical black holes. In such spacetimes the event horizon is teleologically defined while the apparent horizon is non-unique. Thus even if one believes that entropy continues to be well-defined and proportional to horizon area, there are many possible areas to choose from. In this work I will review some recent work that I have done with M. Heller, G. Plewa and M.Spalinski that examines this issue from the perspective of the fluid-gravity correspondence. In this quasi-equilibrium regime the slowly evolving black brane horizons on the gravity side are dual to a perturbed fluid flow. The fluid manifestations of the various horizon definitions can be compared and the blackbrane mechanics is dual to hydro-thermodynamics. In particular, the uncertainty as to which is the "correct" horizon can be interpreted as dual to the inherent freedom in defining an entropy current.

We perform an exact localization calculation for the expectation value of Wilson-'t Hooft line operators in N=2 gauge theories on S^1 x R^3. The expectation values form a quantum mechanically deformed algebra of functions on the Hitchin moduli space by Moyal multiplication. We demonstrate that these expectation values are the Weyl transform of the Verlinde operators, which acts on conformal blocks as difference operators. Our results are also in exact match with the predictions from wall-crossing in the IR effective theory.

In recent years there has been a lot of interest in F-Theory GUTs, mostly considering local models. In this talk I first consider an SU(5) GUT locally at the "point of E_8". The requirements of proton stability and reasonable flavour structure single out exactly two models. However, both models cannot be embedded in a semilocal construction (via the spectral cover approach). This casts doubts on the predictivity of local models.

I will first summarize recent exact localization computations of supersymmetric gauge theories, and then discuss curious connections between SUSY/non-SUSY theories coming from 6d (2,0) theories. I particular, I will focus on our recent proposal relating 3d N=2 theories and 3d SL(2,R) Chern-Simons theories (or more mathematically, geometry of 3-manifolds).