PIRSA:23100073

Analyticity properties of 2d Ising Field Theories

Xu, H. (2023). Analyticity properties of 2d Ising Field Theories. Perimeter Institute. https://pirsa.org/23100073

Xu, Hao-Lan. Analyticity properties of 2d Ising Field Theories. Perimeter Institute, Oct. 03, 2023, https://pirsa.org/23100073 

          @misc{ pirsa_PIRSA:23100073,
            doi = {10.48660/23100073},
            url = {https://pirsa.org/23100073},
            author = {Xu, Hao-Lan},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Analyticity properties of 2d Ising Field Theories},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {oct},
            note = {PIRSA:23100073 see, \url{https://pirsa.org}}
          }

Hao-Lan Xu Stony Brook University

DOI 10.48660/23100073
Collection
Talk Type Scientific Series
Subject

Abstract

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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