A bstract We study modular invariants arising in the fourpoint functions of the stress tensor multiplet operators of the $$ \mathcal{N} $$ N = 4 SU( N ) superYangMills theory, in the limit where N is taken to be large while the complexified YangMills coupling τ is held fixed. The specific fourpoint 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 halfinteger orders in 1 /N , these modular invariants are linear combinations of nonholomorphic 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 lowenergy expansion of themore »
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2D Ising Field Theory in a magnetic field: the YangLee 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 YangLee edge singularity. While the leading singular behavior is controlled by the YangLee 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:
 NSFPAR ID:
 10371693
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2022
 Issue:
 8
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
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