Boundaries and Defects in Quantum Field Theory

We study the quantum work associated with the nonequilibrium quench of an optical lattice as it evolves from initial Mott type states with large potential barriers under the Sine-Gordon Hamiltonian that describes the dynamics of the system when the barriers are suddenly lowered. The calculations are carried out by means of the Boundary Bethe Ansatz approach where the initial and final states of the quench are applied as boundary states on the evolving system. We calculate exactly the Loschmidt amplitude, the fidelity and work distribution characterizing the quenches for different values of the interaction strength.

We probe a generic two dimensional conformal interface via a collider experiment. We measure the energy and charges which are reflected and transmitted through the interface. If the largest symmetry algebra is Virasoro, the average transmitted energy is independent of the details of the initial state, and is fixed in terms of the central charges and of the two-point function of the displacement operator. The situation is more elaborate when extended symmetries are present. We comment on the bounds imposed by positivity of the total energy flux at infinity, and on applications of the result to the physics of steady states.

I will discuss entanglement negativity, an entanglement measure for mixed quantum states, in many-body systems, including lattice quantum systems and quantum field theories. I will also discuss the possible holographic dual description of entanglement negativity in field theories and tensor networks.

The shape deformation of conformal defects is implemented by the displacement operator. In this talk we consider superconformal defects and we provide evidence of a general relation between the two-point function of the displacement and the one-point function of the stress tensor operator. We then discuss the available techniques for the computation of this one-point function. First, we show how it can be related to a deformation of the background geometry. Then we conclude with a discussion of surface defects in four-dimensional N=2 theories, where the chiral algebra provides an additional powerful tool.

The g-theorem is a prominent example of C-theorems in two-dimensional boundary CFT and the extensions are conjectured to hold in higher-dimensional BCFTs. On the other hand, much less is known for C-theorems in a CFT with conformal defects of higher codimensions. I will investigate the entanglement entropy across a sphere and sphere free energy as a candidate for a C-function in DCFT, and show they differ by a universal term proportional to the vev of the stress tensor. Based on this relation, I will propose to use the sphere free energy as a C-function in DCFT. This proposal unifies the previously known theorems and conjectures, and passes several checks, including a few examples in field theories and a holographic proof in simple gravity dual models of DCFTs.

I will review recent results concerning a general class of parametric BPS Wilson loops in ABJM theory. In particular, I will present a proposal for their exact quantum expression in terms of a parametric Matrix Model and discuss their role in the exact calculation of physical quantities like the Bremsstrahlung function and in testing the AdS4/CFT3 correspondence.

We observe that boundary correlators of the elementary scalar field of the Liouville theory defined on rigid AdS2 background are the same as the correlators of the chiral stress tensor of the Liouville CFT on the complex plane restricted to the real line. The same relation generalizes to the conformal abelian Toda theory: correlators of Toda scalars on AdS2 are directly related to those of the chiral W-symmetry generators in the Toda CFT and thus are essentially controlled by the underlying infinite-dimensional symmetry. These may be viewed as examples of AdS2/CFT1 duality where the CFT1 is the chiral half of a 2d CFT. Similar relation applies also to a non-abelian Toda theory containing a Liouville scalar coupled to a 2d sigma-model originating from the SL(2,R)/U(1) gauged WZW model. Here the Liouville scalar is again dual to the chiral stress tensor T while the other two scalars are dual to the parafermionic operators V± of the non-abelian Toda CFT. The duality is checked at the next-to-leading order in the large central charge expansion by matching the chiral CFT correlators of (T,V+,V−) with the boundary correlators of the three Toda scalars given by the tree-level and one-loop Witten diagrams in AdS2. Based on arXiv:1904.12753,1907.01357.

I will overview recent results on the defect CFT corresponding to Wilson loop operators in N=4 SYM theory. In particular, I will review the calculation of defect correlators at strong coupling using the AdS2 string worldsheet, and I will present exact results for correlation functions in a subsector of the defect CFT using localization. I will also discuss a defect RG flow from the BPS to the ordinary Wilson loop, which can be used to provide a test of the "defect F-theorem" for one-dimensional defects.

In this talk, I will briefly discuss the construction of semiclassical 1/2-BPS boundary conditions and duality interfaces in 3d N=2 theories, following work with T. Dimofte and D. Gaiotto. Then, I will sketch some mathematical applications of these codimension-1 defects to the geometry of triangulated 4-manifolds and chiral algebras, based on work with T. Dimofte and building off related advances by Gadde, Gukov, and Putrov. I will also mention recent and ongoing work on generating 2d dualities from dual "sandwich" configurations of 3d theories sandwiched by both left and right boundary conditions.

A four-dimensional abelian gauge theory can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFTs) parametrized by the gauge coupling \tau and by the choice of the CFT in the decoupling limit. Upon performing an Electric-Magnetic duality in the bulk and going to the decoupling limit in the new frame, one finds a different 3d CFT on the boundary, related to the original one by Witten's SL(2, Z) action. In particular the cusps on the real \tau axis correspond to the 3d gauging of the original CFT. We study general properties of this family of BCFTs. We show how to express bulk one and two-point functions, and the hemisphere free-energy, in terms of the two-point functions of the boundary electric and magnetic currents. Finally, upon assuming particle-vortex duality (and its fermionic version), we show how to turn this machinery into a powerful computational tool to study 3d gauge theories.

The partnership between 3D gravity and Chern-Simons theory is well-known and powerful, but many aspects of this relation are unclear. In this talk I'll discuss Wilson lines in Chern-Simons theory and their role in AdS3 gravity. Wilson lines are interesting objects to explore locality in Chern-Simons theory, and how they affect the partnership at the quantum level.

I will start by reviewing the definition and properties of complexity as well as the relevant holographic proposals. I will then describe the results of [1811.12549] where we studied the two holographic complexity proposals for the case of a 2d boundary CFT with a conformal defect using a Randall-Sundrum type model of a thin AdS_2 brane embedded in AdS_3. Our results indicate that this setup can be used to distinguish the two holographic proposals for the complexity. I will also describe results for simple free bosonic field theory models which include two defects on opposite sides of a periodic domain.