# Boundaries in quantum field theory

A boundary conformal field theory (BCFT) is a QFT on a manifold with topological boundary, such as a half-plane, a disk, or a strip, for which the boundary accommodates "reduced" conformal symmetry. Such theories are relevant across a range of fields, from quantum gravity to finite condensed matter systems. My research is concerned with developing and implementing tools with which to answer open questions about BCFT.

Currently, the main problem with which I am concerned is the classification of conformal boundary conditions in 2d BCFT. This is often equivalently phrased in algebraic language, in which conformal boundary conditions are described by CFT states. For a generic CFT, the organizing principle of conformal boundary states is unknown. Using various tools, I aim to probe aspects of this broad open problem.

One tool is the AdS/BCFT correspondence, an adaptation of AdS/CFT which incorporates boundaries. Duality between strongly-coupled BCFT and (semi)classical gravity on a higher-dimensional AdS space requires a boundary called an "end-of-the-world brane" in AdS. Notably, the "dictionary" which translates between quantities in AdS gravity and quantities in BCFT is not as well-developed as that of AdS/CFT, and so part of my work focuses on adaptations of the AdS/CFT dictionary to AdS/BCFT. These adaptations would then teach us about the consequences of having a boundary in a quantum system.

Another tool is the conformal bootstrap, in which we use generic, non-perturbative consequences of conformal symmetry in order to put bounds of various physical data. The bootstrap program in BCFT is still underdeveloped, but in principle it may be used to constrain the space of conformal boundary states.

# Selected publications

S. Biswas, J. Kastikainen, SS, J. Sully, Holographic BCFT spectra from brane mergers. Accepted for publication by Journal of High Energy Physics 11 (2022) 158. arXiv:2209.11227, Sep 2022.

We examine how the dynamics of bulk AdS branes fits into the AdS/BCFT correspondence. In particular, we focus on interactions between branes in the bulk mediated by either scalars or point particles. By computing these interactions, we determine the corresponding dual spectrum of states in the field-theory side of the holographic correspondence. Our work demonstrates that AdS/BCFT is not a "clean" statement of duality between the bulk branes and the field-theoretic boundaries. Rather, the dynamics of branes are the holographic embodiment of nontrivial operators in the dual field theory.

J. Kastikainen, SS, Structure of holographic BCFT correlators from geodesics. Physical Review D 105 (2022) 4, 046007. arXiv:2109.00079, preprint Aug 2021.

Statistical correlations of scalars in holographic CFT are captured to leading order in mass by the length of a geodesic going through the bulk. We extend this "geodesic approximation" to holographic BCFT, finding that one must consider a sum over geodesics which reflect off of the brane any number of times.

# Under review

S. A. Baig, SS, Transport across interfaces in symmetric orbifolds. arXiv:2301.12170, Jan 2023.

We study energy transport across conformal interfaces in 2d symmetric orbifold CFT, a large class of theories in which reproduce many of the features seen through holography. Such interfaces are encoded by boundary states, and so their transport properties capture aspects of associated conformal boundary states. Upon establishing a general recipe for computing transmission and reflection coefficients in free symmetric orbifolds, we then look to the symmetric orbifold theory of a 4-torus sigma model with a simple conformal interface. We use our recipe to approximate the coefficients in the weakly coupled sector. Furthermore, the strongly coupled sector is known to be dual to type IIB supergravity on a Janus-AdS background, and so we use holography to compute transport coefficients in this regime. We then compare the answers from the different sectors together, finding that the transport coefficients capture aspects of boundary states which run in the coupling.

# In progress

P. Pelliconi, B. Radhakrishnan, SS, Boundaries in irrational product theories.

We study boundary states in tensor-product theories of rational CFTs. In principle, such theories are specified completely by their factors. However, while the boundary states in a rational CFT may be written down as a finite list, this is not the case for the tensor product. Indeed, even for minimal-model factors, the product theory may furnish "emergent" boundary conditions which cannot simply be mapped to the conformal-boundary-state spectrum of the factor theories. We find that this is because the primary representations of the factors map to infinite towers of primary representations in the product theory. With this in mind, we set up bootstrap equations with which to constrain the coefficients of boundary states in a given product theory.