A bstract When the SU( N ) $$ \mathcal{N} $$ N = 4 superYangMills (SYM) theory with complexified gauge coupling τ is placed on a round foursphere and deformed by an $$ \mathcal{N} $$ N = 2preserving mass parameter m , its free energy F ( m, τ, $$ \overline{\tau} $$ τ ¯ ) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative $$ {\partial}_m^4F\left(m,\tau, \overline{\tau}\right)\left{{}_m}_{=0}\right. $$ ∂ m 4 F m τ τ ¯ m = 0 of the sphere free energy and the integrated stresstensor multiplet fourpoint function in the $$ \mathcal{N} $$ N = 4 SYM theory. We then apply this exact relation, along with various other constraints derived in previous work (coming from analytic bootstrap, the mixed derivative $$ {\partial}_{\tau }{\partial}_{\overline{\tau}}{\partial}_m^2F\left(m,\tau, \overline{\tau}\right)\left{{}_m}_{=0}\right. $$ ∂ τ ∂ τ ¯ ∂ m 2 F m τ τ ¯ m = 0 , and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large N and large ’t Hooft coupling λ expansion of the $$ \mathcal{N} $$ N = 4 SYM correlator at separated points. In particular, we determine the leading large λ term in the $$ \mathcal{N} $$ N = 4 SYM correlation function at order 1 /N 8 . This is three orders beyond the planar limit.
more »
« less
Onedimensional sectors from the squashed threesphere
A bstract Threedimensional $$ \mathcal{N} $$ N = 4 superconformal field theories contain 1d topological sectors consisting of twisted linear combinations of halfBPS local operators that can be inserted anywhere along a line. After a conformal mapping to a round threesphere, the 1d sectors are now defined on a great circle of S 3 . We show that the 1d topological sectors are preserved under the squashing of the sphere. For gauge theories with matter hypermultiplets, we use supersymmetric localization to derive an explicit description of the topological sector associated with the Higgs branch. Furthermore, we find that the dependence of the 1d correlation functions on the squashing parameter b can be removed after appropriate rescalings. One can introduce real mass and FayetIliopolous parameters that, after appropriate rescalings, modify the 1d theory on the squashed sphere precisely as they do on the round sphere. In addition, we also show that when a generic 3d $$ \mathcal{N} $$ N = 4 theory is deformed by real mass parameters, this deformation translates into a universal deformation of the corresponding 1d theory.
more »
« less
 Award ID(s):
 2111977
 NSFPAR ID:
 10348506
 Date Published:
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2022
 Issue:
 8
 ISSN:
 10298479
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this


A bstract We study which bulk couplings contribute to the S 3 free energy F ( $$ \mathfrak{m} $$ m ) of threedimensional $$ \mathcal{N} $$ N = 2 superconformal field theories with holographic duals, potentially deformed by boundary realmass parameters m. In particular, we show that F ( $$ \mathfrak{m} $$ m ) is independent of a large class of bulk couplings that include nonchiral Fterms and all Dterms. On the other hand, in general, F ( $$ \mathfrak{m} $$ m ) does depend nontrivially on bulk chiral Fterms, such as prepotential interactions, and on bulk realmass terms. These conclusions can be reached solely from properties of the AdS superalgebra, $$ \mathfrak{osp} $$ osp (24). We also consider massive vector multiplets in AdS, which in the dual field theory correspond to long singletrace superconformal multiplets of spin zero. We provide evidence that F ( $$ \mathfrak{m} $$ m ) is insensitive to the vector multiplet mass and to the interaction couplings between the massive vector multiplet and massless ones. In particular, this implies that F ( $$ \mathfrak{m} $$ m ) does not contain information about scaling dimensions or OPE coefficients of singletrace long scalar $$ \mathcal{N} $$ N = 2 superconformal multiplets.more » « less

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 the fourgraviton amplitude in type IIB superstring theory in tendimensional flat space and have interesting implications for the structure of the analogous expansion in AdS 5 × S 5 .more » « less

A bstract We study the massdeformed sphere free energy of threedimensional $$ \mathcal{N} $$ N = 2 superconformal field theories with holographic duals. Building on previous observations, we conjecture a proportionality relation between the sphere free energy on the boundary and the prepotential of the fourdimensional $$ \mathcal{N} $$ N = 2 supergravity theory in the bulk. We verify this formula by explicit computation in several examples of supergravity theories with vector multiplets and hypermultiplets.more » « less

A bstract We initiate a study of the holographic duals of a class of fourdimensional $$ \mathcal{N} $$ N = 2 superconformal field theories that are engineered by wrapping M5branes on a sphere with an irregular puncture. These notably include the stronglycoupled field theories of ArgyresDouglas type. Our solutions are obtained in 7d gauged supergravity, where they take the form of a warped product of AdS 5 and a “halfspindle.” The irregular puncture is modeled by a localized M5brane source in the internal space of the gravity duals. Our solutions feature a realization of supersymmetry that is distinct from the usual topological twist, as well as an interesting Stückelberg mechanism involving the gauge field associated to a generator of the isometry algebra of the internal space. We check the proposed duality by computing the holographic central charge, the flavor symmetry central charge, and the dimensions of various supersymmetric probe M2branes, and matching these with the dual ArgyresDouglas field theories. Furthermore, we compute the large N ’t Hooft anomalies of the field theories using anomaly inflow methods in Mtheory, and find perfect agreement with the proposed duality.more » « less