Entanglement entropy has long served as a key diagnostic of topological order in (2+1) dimensions. In particular, the topological entanglement entropy captures a universal quantity (the total quantum dimension) of the underlying topological order. However, this information alone does not uniquely determine which topological order is realized, indicating the need for more refined probes. In...
I will discuss the question posed in the title in the context of 2D CFTs. In particular, I will conjecture and provide some evidence that the answer is “always” if the two CFTs have the same left- and right-moving central charges, so long as one accepts topological interfaces of infinite quantum dimension. I will also illustrate how a topological interface between Theory A and Theory B allows...
It is a well-established fact that any conformal field theory with a gap in the twist spectrum must contain families of multi-twist operators, whose spectrum at large spin approaches that of generalized free theory. In presence of a defect, this statement gets enriched by the existence of families of defect operators known as transverse derivative operators. In this talk, we aim to discuss...
In this talk, I will explain that the (E_8)_1 WZW model has Haagerup symmetry H_3, and that gauging H_3 gives a c = 8 theory with Z(H_3) symmetry. In addition, I will suggest a relation to theories with H_3 symmetry at c = 2 and c = 6, complementing the discussion with new modular bootstrap results.
I will give an overview of recent developments using the Symmetry TFT to characterize phases of matter with categorical symmetries, which turns out to have a very curious, and potentially far-reaching implication in the construction of universal quantum computation in 2D lattice models -- namely the construction of transversal phase gates.
This gives a surprising connection between advances...
Lattice field theory provides one of the most reliable nonperturbative regularizations of quantum field theory. Meanwhile, the eta invariant of the Dirac operator, defined as a regularized sum of the signs of its eigenvalues, plays an important role in symmetry-protected topological phases and in anomalies in quantum field theories. In this talk, we investigate how the eta invariant can be...
Defect conformal field theories (DCFTs) provide a universal framework for describing the low energy interaction of heavy degrees of freedom with light excitations. In a DCFT part of the Poincaré symmetry is broken explicitly.
However, the fundamental laws of our world are Poincaré invariant and any breaking of space-time symmetries must be spontaneous. In particular, extended and thin objets...
We study quenched disorder localized on a p-dimensional subspacetime in a d-dimensional conformal field theory. Motivated by the logarithmic behavior often associated with disorder, we introduce a defect setup in which bulk local operators transform in ordinary conformal representations, while defect local operators assemble into logarithmic multiplets. We refer to such objects as logarithmic...
In this talk, I will consider "bottom-up" (toy) models of Einstein gravity with either gravitating domain walls or end-of-the-world (ETW) branes. In AdS/CFT language, these bulk objects are holographically dual to codimension-one conformal defects and boundaries, respectively. Depending on which type of model, one can study notions of either an AdS/DCFT or an AdS/BCFT correspondence. From...
Gapped phases of matter at long distance are described by TQFTs. In this talk I will discuss a physical interpretation of the TQFT partition functions in terms of the multipartite entanglement of the ground state. Based on joint work with Abhijit Gadde and Pavel Putrov.
Symmetry can be realized in an anomalous fashion on the dynamical defects of a theory. These "defect anomalies" are exact non-perturbative defect data which constrain their physics in several ways.
In this talk, I explain how defect anomalies can be detected in scattering experiments, where they are responsible for processes in which local particles in the in-state are morphed into nonlocal...
We would like to report on our recent study on a mathematical relation between the Atiyah-Patodi-Singer index on a manifold with boundary and the spectral flow on a closed manifold with interfaces. The talk is based on the works in collaboration with S. Aoki, M. Furuta, S. Matsuo, T. Onogi and S. Yamaguchi.
In QED coupled to four or more Dirac fermions, the scattering of fermions off a target monopole is exotic; the out state is not in the Fock space one started with. In the s-wave reduced version of the problem, I will describe how one would measure such an out state.
I will present recent advances in the understanding conserved defects in 2d CFTs. Both topological and non-topological defect may give rise to conserved quantities in deformed 2d CFT. I will characterize a class of translational invariant defects from the UV to the IR of an RG flows triggered by relevant perturbation of 2d CFTs. On the way I will discuss various properties of these flows in...
Integrability of planar N=4 super-Yang-Mills (SYM) theory enables exact computations of unprotected observables, even with the insertion of certain extended operators. While integrability techniques have been successfully applied to some domain walls and line defects, it is an open question whether there are any integrable surface defects in N=4 SYM theory. In this talk, I will examine a class...
This talk focuses on the gravity dual of CFTs in networks (AdS/NCFT). We prove that the junction condition on the Net-brane leads to conservation laws at network nodes. Additionally, we discuss various proposals for network entropy, confirm that the type I and II network entropies obey the holographic g-theorem, and show that the type III network entropy is non-negative. We show that AdS/NCFT...
