Quantum Fields and Strings

Several years ago, Nayak and Else argued that Symmetry Protected Topological phases in d dimensions can be classified using non-on-site actions of the symmetry group in d-1 dimensions. Such non-on-site actions can have an “anomaly”, in the sense that the symmetry action cannot be consistently localized. This anomaly is similar but distinct from ’t Hooft anomaly in QFT. Nayak and Else assumed that the symmetry group is finite and the non-on-site action is given by a finite-depth local unitary circuit. I will explain how to generalize the construction of the anomaly index in two directions: to Lie groups as well as to arbitrary actions which preserve locality. For simplicity, I will only discuss the one-dimensional case. One can prove that a nonzero anomaly index prohibits any invariant 1d Hamiltonian from having invariant ground states. This is similar to ’t Hooft anomaly matching in QFT. Lieb-Schultz-Mattis-type theorems arise as a special case where the symmetry group involves translations. This is joint work with Nikita Sopenko.

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Zoom link https://pitp.zoom.us/j/95661517248?pwd=SkMxUFJWTG56SG9hVlNiNS9yeEVrQT09

I will explore subtle aspects of rank-one 4d N=2 supersymmetric QFTs through their low-energy Coulomb-branch physics. The low-energy Lagrangian is famously encoded in "the Seiberg-Witten (SW) curve", which is a one-parameter family of elliptic curves. Here I will explain precisely how "global" aspects of the SQFT such as its spectrum of lines, which cannot be read off from the Lagrangian, are encoded into the SW curve -- more precisely, how they are encoded in its Mordell-Weil group of rational sections. In particular, I will
discuss in detail the difference between the pure SU(2) and the pure SO(3) N=2 SYM theories from this low-energy perspective. I will also comment on the global forms of rank-one 5d SCFTs compactified on a circle.

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Zoom link https://pitp.zoom.us/j/94967350368?pwd=SHZZUnZNL3ZveFc3NElCaVc5YkY3Zz09

We investigate the nature of the Giddings-Strominger wormhole in axion gravity, whose stability remains contested despite previous work in this direction. Unlike what is done in these works, we follow a Lorentzian approach which directly addresses the factorization problem. To probe the thermodynamic stability of wormholes in the gravitational path integral, we look for fixed-area saddle points. However, taking care to choose the appropriate boundary conditions, we find that there are no fixed-area axion wormholes in Lorentzian signature. We then discuss how we could go beyond this analysis, considering off-shell axion wormhole configurations with fixed-length.

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Zoom link https://pitp.zoom.us/j/98119789932?pwd=N1RCanJCdk56eWJ3RHJCRG5KU21lQT09

Spacetime inversion symmetries such as parity and time reversal play a central role in physics, but they are usually treated as global symmetries. In quantum gravity there are no global symmetries, so any spacetime inversion symmetries must be gauge symmetries. In particular this includes CRT symmetry (in even
dimensions usually combined with a rotation to become CPT), which in quantum field theory is always a symmetry and seems likely to be a symmetry of quantum gravity as well. I'll discuss what it means to gauge a spacetime inversion symmetry, and explain some of the more unusual consequences of doing this. In particular I'll argue that the gauging of CRT is automatically implemented by the sum over topologies in the Euclidean gravity path integral, that in a closed universe the Hilbert space of quantum gravity must be a real vector space, and that in Lorentzian signature manifolds which are not time-orientable must be included as valid configurations of the theory.

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Zoom link https://pitp.zoom.us/j/98089579253?pwd=NDBhUjBUTTEwT0R5YmhYVElZenJtZz09

Using a novel version of the gravitational path integral for compact spatial regions at a moment of time symmetry, I argue that a region of space can encode a larger one. In particular, I show that the entanglement entropy of a region of space equals the area of the boundary of the smallest region that contains it. The key insight is to include the effects of the gravitational edge modes associated with the region in the path integral. This result is consistent with a recent conjecture by Bousso and Penington.

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Zoom link https://pitp.zoom.us/j/93301151464?pwd=Z2t5QlpUQ3hoaEkwQlFZS2tITGpEQT09

Abstract TBA

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Zoom link https://pitp.zoom.us/j/97897878725?pwd=dHZNUEc5cVlkU2ZNdU14bEhIRmFPZz09

Costello, Witten and Yamazaki proposed a 4d Chern-Simons theory as a unified way to engineer integrable models. In the presence of 'Disorder' defects (for non-ultralocal 2d theories), this correspondence has been established only classically. As a first quantum check, I will derive the matching of 1-loop divergences between the 4d and 2d theories. My assumptions are general and seem to isolate sigma-models among the 2d theories. (Based on 2309.16753)

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Zoom link https://pitp.zoom.us/j/99362983669?pwd=NE1uQ3FmWityQ1R0NUVnZkRPZTRUdz09

In the last few years, a remarkable link has been established between the soft theorems and asymptotic symmetries of quantum field theories: soft theorems are Ward identities of the asymptotic symmetry generators. In quantum electrodynamics, Weinberg's soft photon theorem is nothing but the Ward identity of a gauge transformation whose parameter is non-trivial at infinity. Likewise, Low's tree-level subleading soft photon theorem is the Ward identity of a gauge transformation whose parameter diverges linearly at infinity. More recently, it has been shown that Low's theorem receives loop corrections that are logarithmic in soft photon energy. Then, it is natural to ask whether such corrections are associated with some asymptotic symmetry of the S-matrix. There have been proposals for conserved charges whose Ward identities yield the loop-corrected soft theorems, but a clear symmetry interpretation remains elusive. We explore this question in the context of scalar QED, in hopes of shedding light on the connection between asymptotic symmetries and loop-corrected soft theorems.

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Zoom link https://pitp.zoom.us/j/94420835190?pwd=dEpOSHluRzFpVTg3Qm10OS9PTTU3dz09

We discuss c-functions and their holographic counterpart for 2d field theories with Carrollian conformal fixed points in the UV and the IR, and construct asymptotically flat domain wall solutions of 3d Einstein-dilaton gravity that model holographic RG flows. arXiv: 2309.11539

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Zoom link https://pitp.zoom.us/j/94223624920?pwd=T3pxOGxnRVFVbGVnZnRuZ2NSTm8wZz09

Abstract TBA

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Zoom link: https://pitp.zoom.us/j/97133792880?pwd=d1pxMThTd1R3YjZUVENiOWRLOUZpZz09

In this talk, I will discuss the analyticity properties of 2d Ising field theories (IFTs). I will start with a short introduction to 2d Ising field theory, which is the continuous limit of the 2d Ising model on square lattice. Then the different spectrum scenarios for high-T and low-T domains will be introduced. Generally speaking, an IFT which sits not at the critical temperature and has a non-vanishing external field is neither solvable nor integrable. However, it's possible to look into the analytical properties of various quantities in the theory space, then further non-perturbative information can be extracted. I will focus on the analyticity properties for mass of the first excitation, and discuss its critical behaviours and dispersion relations in both ordered and disordered phase. Finally, if time allowed, I will switch to the analyticity properties of the analytical structure of S-matrices, and show various related interesting phenomenons together with unsolved problems

References:
[1], Ising field theory in a magnetic field: Analytic properties of the free energy, P. Fonseca and A. Zamolodchikov, hep-th/0112167 [hep-th].
[2], Ising Spectroscopy II: Particles and poles at T > Tc, A. Zamolodchikov, 1310.4821 [hep-th].
[3], 2D Ising Field Theory in a magnetic field: the Yang-Lee singularity, H. Xu and A. Zamolodchikov, 2203.11262 [hep-th].
[4], On the S-matrix of Ising field theory in two dimensions, B. Gabai and X. Yin, 1905.00710 [hep-th]
[5], Ising field theory in a magnetic field: phi^3 coupling at T > Tc, H. Xu and A. Zamolodchikov, 2304.07886 [hep-th]
[6], Corner Transfer Matrix Approach to the Yang-Lee Singularity in the 2D Ising Model in a magnetic field, V.V.Mangazeev, B.Hagan and V.V.Bazhanov, 2308.15113 [hep-th]
[7], Ising Field Theory in a Magnetic Field: Extended analyticity properties of M1, H. Xu, in preparation.

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Zoom link: https://pitp.zoom.us/j/97062411964?pwd=TWFHU0I5UGw3eXZjZzRHUEFnbjlydz09