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.

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

Under review

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