A bstract We study modular invariants arising in the four-point functions of the stress tensor multiplet operators of the $$ \mathcal{N} $$ N = 4 SU( N ) super-Yang-Mills theory, in the limit where N is taken to be large while the complexified Yang-Mills coupling τ is held fixed. The specific four-point functions we consider are integrated correlators obtained by taking various combinations of four derivatives of the squashed sphere partition function of the $$ \mathcal{N} $$ N = 2 ∗ theory with respect to the squashing parameter b and mass parameter m , evaluated at the values b = 1 and m = 0 that correspond to the $$ \mathcal{N} $$ N = 4 theory on a round sphere. At each order in the 1 /N expansion, these fourth derivatives are modular invariant functions of ( τ, $$ \overline{\tau} $$ τ ¯ ). We present evidence that at half-integer orders in 1 /N , these modular invariants are linear combinations of non-holomorphic Eisenstein series, while at integer orders in 1 /N , they are certain “generalized Eisenstein series” which satisfy inhomogeneous Laplace eigenvalue equations on the hyperbolic plane. These results reproduce known features of the low-energy expansion of themore »
This content will become publicly available on August 1, 2023
2D Ising Field Theory in a magnetic field: the Yang-Lee singularity
A bstract We study Ising Field Theory (the scaling limit of Ising model near the Curie critical point) in pure imaginary external magnetic field. We put particular emphasis on the detailed structure of the Yang-Lee edge singularity. While the leading singular behavior is controlled by the Yang-Lee fixed point (= minimal CFT $$ \mathcal{M} $$ M 2 / 5 ), the fine structure of the subleading singular terms is determined by the effective action which involves a tower of irrelevant operators. We use numerical data obtained through the “Truncated Free Fermion Space Approach” to estimate the couplings associated with two least irrelevant operators. One is the operator $$ T\overline{T} $$ T T ¯ , and we use the universal properties of the $$ T\overline{T} $$ T T ¯ deformation to fix the contributions of higher orders in the corresponding coupling parameter α . Another irrelevant operator we deal with is the descendant L_ 4 $$ \overline{L} $$ L ¯ _ 4 ϕ of the relevant primary ϕ in $$ \mathcal{M} $$ M 2 / 5 . The significance of this operator is that it is the lowest dimension operator which breaks integrability of the effective theory. We also establish analytic more »
- Award ID(s):
- 1915093
- Publication Date:
- NSF-PAR ID:
- 10371693
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2022
- Issue:
- 8
- ISSN:
- 1029-8479
- Sponsoring Org:
- National Science Foundation
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