A new duality between $$ \mathcal{N} $$ = 8 superconformal field theories in three dimensions

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117

We develop an approach to the study of Coulomb branch operators in 3D N = 4 gauge theories and the associated quantization structure of their Coulomb branches. This structure is encoded in a one-dimensional TQFT subsector of the full 3D theory, which we describe by combining several techniques and ideas. The answer takes the form of an associative and noncommutative star product algebra on the Coulomb branch. For "good" and "ugly" theories (according to the Gaiotto-Witten classification), we also exhibit a trace map on this algebra, which allows for the computation of correlation functions and, in particular, guarantees that the star product satisfies a truncation condition. This work extends previous work on abelian theories to the non-abelian case by quantifying the monopole bubbling that describes screening of GNO boundary conditions. In our approach, monopole bubbling is determined from the algebraic consistency of the OPE. This also yields a physical proof of the Bullimore-Dimofte-Gaiotto abelianization description of the Coulomb branch.

Section: E3 Theories With No Adjointsmentioning

confidence: 99%

Coulomb branch quantization and abelianized monopole bubbling

Dedushenko

Fan

Pufu

et al. 2019

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117

“…Instead, as is standard in the Mellin space literature, we use the lightcone expansion U 1 for fixed V . The conformal blocks are expanded as 9) where the lightcone blocks g…”

Section: Extracting Cft Datamentioning

confidence: 99%

AdS4/CFT3 for unprotected operators

Chester

2018

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Abstract:We consider the four-point function of the lowest scalar in the stress-energy tensor multiplet in N = 8 ABJ(M) theory [1,2]. At large central charge c T ∼ N 3/2 , this correlator is given by the corresponding holographic correlation function in 11d supergravity on AdS 4 × S 7 . We use Mellin space techniques to compute the leading 1/c T correction to anomalous dimensions and OPE coefficients of operators that appear in this holographic correlator. For half and quarter-BPS operators, we find exact agreement with previously computed localization results. For the other BPS and non-BPS operators, our results match the N = 8 numerical bootstrap for ABJ(M) at large c T , which provides a precise check of unprotected observables in AdS/CFT.

“…For certain theories, such as ABJM with k = 1, a Lagrangian was derived for this 1d sector that could be used to compute OPE coefficients of half-BPS operators as expectation values of n-body operators in the matrix model [29]. For small N , the integrals in these expectation values were evaluated explicitly in [30,31]. A certain half-BPS operator that appears in the stress-tensor correlator was related to ∂ 4 m i log Z m=0 using the 1d theory in [25], so this OPE coefficient could be computed to all orders in 1/N for any k using the Fermi gas result for Z(m i ).…”

Section: Introductionmentioning

confidence: 99%

3d $$ \mathcal{N} $$ = 4 OPE coefficients from Fermi gas

Chester

Kalloor

Sharon

2020

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The partition function of a 3d N = 4 gauge theory with rank N can be computed using supersymmetric localization in terms of a matrix model, which often can be formulated as an ideal Fermi gas with a non-trivial one-particle Hamiltonian. We show how OPE coefficients of protected operators correspond in this formalism to averages of n-body operators in the Fermi gas, which can be computed to all orders in 1/N using the WKB expansion. We use this formalism to compute OPE coefficients in the U(N) k × U(N) −k ABJM theory as well as the U(N) theory with one adjoint and N f fundamental hypermultiplets, both of which have weakly coupled M-theory duals in the large N and finite k or N f regimes. For ABJM we reproduce known results, while for the N f theory we compute the all orders in 1/N dependence at finite N f for the coefficient c T of the stress tensor two-point function.