Transport coefficients and universality in hot strongly coupled gauge theories

The gauge/gravity duality provides a valuable opportunity to study the behavior of relativistic fluids described by some strongly-interacting non-Abelian gauge theories. However, as yet no gravity duals are known for the field theories that are currently used to describe nature. Thus, it is particularly interesting to search for universal properties of theories with gravity duals. This dissertation discusses a broad class of theories with gravity duals, and it is shown that at high temperatures, the speed of sound squared is bounded from above by one-third of the speed of light squared. It is conjectured that this may be a universal property of theories with gravity duals. It is also shown that the temperature dependence of a number of transport coefficients takes a universal form in the high-temperature limit. In particular, in a high-temperature expansion, the power law of the leading correction away from the infinite temperature limit is universal for all of the transport coefficients, and is the same as that of the speed of sound squared

Searching for Fermi Surfaces in Super-QED

The exploration of strongly-interacting finite-density states of matter has been a major recent application of gauge-gravity duality. When the theories involved have a known Lagrangian description, they are typically deformations of large $N$ supersymmetric gauge theories, which are unusual from a condensed-matter point of view. In order to better interpret the strong-coupling results from holography, an understanding of the weak-coupling behavior of such gauge theories would be useful for comparison. We take a first step in this direction by studying several simple supersymmetric and non-supersymmetric toy model gauge theories at zero temperature. Our supersymmetric examples are $\mathcal{N}=1$ super-QED and $\mathcal{N}=2$ super-QED, with finite densities of electron number and R-charge respectively. Despite the fact that fermionic fields couple to the chemical potentials we introduce, the structure of the interaction terms is such that in both of the supersymmetric cases the fermions do not develop a Fermi surface. One might suspect that all of the charge in such theories would be stored in the scalar condensates, but we show that this is not necessarily the case by giving an example of a theory without a Fermi surface where the fermions still manage to contribute to the charge density.Comment: 37 pages, 3 figures. V3: minor clarifications added, version to appear in JHE

Vacuum structure of Yang-Mills theory as a function of θ\theta

It is believed that in $SU(N)$ Yang-Mills theory observables are $N$-branched functions of the topological $\theta$ angle. This is supposed to be due to the existence of a set of locally-stable candidate vacua, which compete for global stability as a function of $\theta$. We study the number of $\theta$ vacua, their interpretation, and their stability properties using systematic semiclassical analysis in the context of adiabatic circle compactification on $\mathbb{R}^3 \times S^1$. We find that while observables are indeed N-branched functions of $\theta$, there are only $\approx N/2$ locally-stable candidate vacua for any given $\theta$. We point out that the different $\theta$ vacua are distinguished by the expectation values of certain magnetic line operators that carry non-zero GNO charge but zero 't Hooft charge. Finally, we show that in the regime of validity of our analysis YM theory has spinodal points as a function of $\theta$, and gather evidence for the conjecture that these spinodal points are present even in the $\mathbb{R}^4$ limit.Comment: 33 pages, 6 figures. v3: added reference

Spectral sum rules for confining large-N theories

We consider asymptotically-free four-dimensional large-$N$ gauge theories with massive fermionic and bosonic adjoint matter fields, compactified on squashed three-spheres, and examine their regularized large-$N$ confined-phase spectral sums. The analysis is done in the limit of vanishing 't Hooft coupling, which is justified by taking the size of the compactification manifold to be small compared to the inverse strong scale $\Lambda^{-1}$. Our results motivate us to conjecture some universal spectral sum rules for these large $N$ gauge theories.Comment: 25 pages, 2 figures. v2: fixed typos, added references, and some minor improvements to discussio