Quantum Fields and Strings

Wilson loops are important observables in gauge theory. In this talk, we study half-BPS Wilson loops of a large class of five dimensional supersymmetric quiver gauge theories with 8 supercharges. The Wilson loops are codimension 4 defects of the quiver gauge theory, and their interaction with self-dual instantons is captured by a 1d ADHM quantum mechanics. We compute the partition function as its Witten index. It turns out that we can understand the 5d physics in 3d gauge theory terms. This comes about from so-called gauge/vortex duality; namely, we study the vortices on the Higgs branch of the 5d theory, and reinterpret the physics from the point of view of the vortices. This perspective has an advantage: it has a dual description in terms of "deformed" Toda Theory on a cylinder, in the Coulomb gas formalism. We show that the gauge theory partition function is equal to a (chiral) correlator of the deformed Toda Theory, with stress tensor and higher spin operator insertions. We derive all the above results from type IIB string theory, compactified on a resolved ADE singularity X times a cylinder with punctures. The 5d quiver gauge theory arises as the low energy limit of a system of D5 branes wrapping various two-cycles of X, the Wilson loops are D1 branes, and the duality to Toda theory emerges after introducing additional D3 branes.

Black hole (more generally, horizon) thermodynamics is a window into quantum gravity. Can horizon thermodynamics---and ultimately quantum gravity---be quasi-localized? A special case is the static patch of de Sitter spacetime, known since the work of Gibbons and Hawking to admit a thermodynamic equilibrium interpretation. It turns out this interpretation requires that a negative temperature is assigned to the state. I'll discuss this example, and its generalization to all causal diamonds in maximally symmetric spacetimes. This story includes a Smarr formula and first law of causal diamonds, analogous to those of black hole mechanics. I’ll connect this first law to the statement that generalized entropy in a small diamond is maximized in the vacuum at fixed volume.

This talk is about a new type of string theory with a non-relativistic conformal field theory on the world-sheet, as well as a non-relativistic target space geometry. Starting with the relativistic Polyakov action with a fixed momentum along a non-compact null-isometry, we can take a scaling limit that gives the non-relativistic string, including an interesting intermediate step. This can in particular be applied to a string on AdS5 x S5. In this case the scaling limit realizes a limit of AdS/CFT that on the field theory side gives a quantum mechanical theory known as Spin Matrix theory. We review that Spin Matrix theory is a finite-N version of nearest neighbor spin chains, from which one can find a long-wavelength semi-classical description using sigma-model such as the Landau-Lifshitz sigma-model. Hence, we can show that both sides of the AdS/CFT gives, in this limit, equivalent non-relativistic sigma-models that we are able to write down in a fully covariant manner, and show that it has a non-relativistic local symmetry that realizes the Galilean Conformal Algebra (GCA). This suggests that one has a holographic duality between the quantum mechanical theory of Spin Matrix theory, and the non-relativistic string. This could provide a more tractable holographic duality in which one can study the emergence of non-relativistic strings, geometry and gravity.

2D CFTs have an infinite set of commuting conserved charges, known as the quantum KdV charges. There is a generalised Gibbs ensemble for these theories where we turn on chemical potentials for these charges. I will describe some partial results on calculating this partition function, both in the limit of large charges and perturbatively in the chemical potentials. 

The partition function of three-dimensional N=2 SCFTs on circle bundles of closed Riemann surfaces \Sigma_g was recently computed via supersymmetric localization. In this talk I will describe supergravity solutions having as conformal boundary such circle bundle. These configurations are solutions to N=2 minimal gauged supergravity in 4d and pertain to the class of AdS-Taub-NUT and AdS-Taub-Bolt preserving 1/4 of the supersymmetries. I will discuss the conditions for the uplift of these solutions to M-theory and I provide the expression for the on-shell action of the Bolt solutions, computed via holographic renormalization. I will show that, when the uplift condition is satisfied, the Bolt free energy matches with the large N limit of the partition function of the corresponding dual field theory. I will finally comment on possible subtleties that arise in our framework when a given boundary geometry admits multiple bulk fillings.

Melonic tensor model is a new type of solvable model, where the melonic Feynman diagrams dominate in the large N limit. The melonic dominance, as well as the solvability of the model, relies on a special type of interaction vertex, which generically would not be preserved under renormalization group flow. I will discuss a class of 2d N=(2,2) melonic tensor models, where the non-renormalization of the superpotential protects the melonic dominance. Another important feature of our models is that they admit a novel type of deformations which gives a large IR conformal manifold. At generic point of the conformal manifold, all the flavor symmetries (including the O(N)^{q-1} symmetry) are broken and all the flat directions in the potential are lifted. I will also discuss how the operator spectrum and the chaos exponent depend on the deformation parameters.

In string backgrounds with flux and branes, there are subtleties in identifying the independent, globally-defined degrees of freedom due to required gauge patching, which we illustrate with background flux. Work by Cariglia and Lechner (extending Dirac and Teitelboim) allows separation of D-brane and flux degrees of freedom without doubling the gauge sector in a democratic formalism. We review the Cariglia-Lechner formalism and adapt it for compactifications, point out some previously unremarked features, and give alternate derivations of some new terms in the 10D (and 11D) supergravity actions in the presence of branes. Along the way, we will discuss how to integrate gauge potentials that are only locally defined. Finally, we show how to find the independent degrees of freedom and derive their equations of motion.

The near horizon region of any black hole looks like flat space and displays an approximate Poincare symmetry. We study the way these symmetries are realized for near extremal black holes.

We construct SL(2) generators that move matter fields relative to the boundaries. The construction is exact to all orders in the gravitational coupling. We also display an approximate realization of these generators in terms of simple operators defined at the boundary. These can also be realized in the boundary quantum mechanical theory. We also discuss the realization of these in the SYK model.

Defects and their RG flows play an important role in many systems, with perhaps the most famous example being the Kondo effect. We study Kondo-like interface flows in D1/D5 holography from the point of view of both probe branes and of the corresponding backreacted supergravity solutions.

I will discuss the computation of second-order terms in the entanglement entropy and subregion complexity for a spherical entangling region in the AdS black hole background relative to pure AdS. I will suggest an extension of the conjectured relationship between subregion complexity and Fisher information into a relation that is reminiscent of the first law of thermodynamics. By analogy, entanglement and complexity play the roles of heat and work, respectively. Time permitting, I will also discuss the computation of third- and fourth-order terms in the relative entropy.