Talks

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

The Callan Rubakov Effect describes the interaction between (massless) fermions and a smooth monopole in 4d gauge theory. In this scenario, the fermions can probe the UV physics inside the monopole core which leads to interesting effects such as proton decay in GUT models. However, the monopole-fermion scattering appears to lead to out-states that are not in the perturbative Hilbert space. In this talk, we will review this issue and propose a new physical mechanism that resolves this long-standing confusion.

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Zoom link: https://pitp.zoom.us/j/93551249905?pwd=REJvOUtTMlh6RU0vRjZnRVdZckgyZz09

A consequence of the works of Costello and Lurie is that the Hochschild chain complex of a Calabi-Yau category admit the structure of a framed E_2 algebra (the genus zero operations). I will describe a new algebraic point of view on these operations which admits generalizations to the setting of relative Calabi-Yau structures, which do not seem to fit into the framework of TQFTs. In particular, we obtain a generalization of string topology to manifolds with boundary, as well as interesting operations on Hochschild homology of Fano varieties. Time permitting, I will explain some applications to quiver varieties. This is joint work with Christopher Brav.

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Zoom link: https://pitp.zoom.us/j/97363589637?pwd=T25YS0ZYQlBSWm5maXhQTklpSm50UT09

Fermi liquid theory is a cornerstone of condensed matter physics. I will show how to formulate Fermi liquid theory as an effective field theory. In this approach, the space of low-energy states of a Fermi liquid is identified with a coadjoint orbit of the group of canonical transformations. The method naturally leads to a nonlinear bosonized description of the Fermi liquid with nonlinear corrections fixed by the geometry of the Fermi surface. I will present that the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. The approach can be extended to encompass non-Fermi liquids, which correspond to strongly interacting fixed points obtained by deforming Fermi liquids with relevant interactions. I will also discuss how Berry curvature can be captured in the effective field theory approach.

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Zoom link: https://pitp.zoom.us/j/95381972217?pwd=Ni9iQ2hrUVNnWTJERDRmZk9GaW1jZz09

Weyl geometry is a natural extension of conformal geometry with Weyl covariance mediated by a Weyl connection. We generalize the Fefferman-Graham (FG) ambient construction for conformal manifolds to a corresponding construction for Weyl manifolds. We first introduce the Weyl-ambient metric motivated by the Weyl-Fefferman-Graham (WFG) gauge, which is a generalization of the FG gauge for asymptotically locally AdS (AlAdS) spacetimes. Then, the Weyl-ambient space as a pseudo-Riemannian geometry induces a codimension-2 Weyl geometry. Through the Weyl-ambient construction, we investigate Weyl-covariant quantities on the Weyl manifold and define Weyl-obstruction tensors. We show that Weyl-obstruction tensors appear as poles in the Fefferman-Graham expansion of the AlAdS bulk metric for even boundary dimensions. Under holographic renormalization, we demonstrate that Weyl-obstruction tensors can be used as the building blocks for the Weyl anomaly of the dual quantum field theory.

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Zoom link https://pitp.zoom.us/j/91781363979?pwd=NlhjTVlHTlhMSTcxYnk5eExkTWFqdz09

Unimodularity is a classical notion shows up in various fields like linear algebra, lattices, Poisson algebras, etc. In this talk, we focus on unimodular Hopf algebras and unimodular tensor categories. We will introduce unimodular module categories and use them to construct Frobenius algebras and unimodular tensor categories. These ideas will be illustrated with examples drawn from Hopf algebras.

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Zoom link https://pitp.zoom.us/j/98477599322?pwd=UDJmTklMTGxGODJZTm1Xc1VhL2tDdz09