$S$-duality of boundary conditions in ${\mathcal N}=4$ super Yang-Mills theory

Gaiotto, Davide; Witten, Edward

doi:10.4310/atmp.2009.v13.n3.a5

Cited by 704 publications

(1,805 citation statements)

References 46 publications

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“…For our description, we only need to assume that boundary conditions exist that allow for a coupling to this four-dimensional N = 2 theory living on the boundary of AdS 5 . This is somewhat similar to the boundary conditions of the N = 4 SYM theory on AdS 4 , which allow for a coupling to general threedimensional N = 4 SCFTs living on the boundary [38,39]. However, note that in our case the theory on the boundary is not precisely conformal by itself, but rather the SU(K) gauge theory has a non-zero beta function (even after the coupling to P (K)) which must be precisely canceled by its coupling to the bulk fields.…”

Section: A Simpler Description Of the Physics On Adsmentioning

confidence: 60%

Rigid holography and six-dimensional N = 2 0 $$ \mathcal{N}=\left(2,0\right) $$ theories on AdS5 × S $$ \mathbb{S} $$ 1

Aharony

Berkooz

Rey

2015

J. High Energ. Phys.

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Field theories on anti-de Sitter (AdS) space can be studied by realizing them as low-energy limits of AdS vacua of string/M theory. In an appropriate limit, the field theories decouple from the rest of string/M theory. Since these vacua are dual to conformal field theories, this relates some of the observables of these field theories on AdS space to a subsector of the dual conformal field theories. We exemplify this 'rigid holography' by studying in detail the six-dimensional N = (2, 0) A K−1 superconformal field theory (SCFT) on AdS 5 ×S 1 , with equal radii for AdS 5 and for S 1 . We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on AdS 5 × S 5 /Z K . On R 4,1 × S 1 , this six-dimensional theory has a 5(K − 1)-dimensional moduli space, with unbroken five-dimensional SU(K) gauge symmetry at (and only at) the origin. On AdS 5 × S 1 , the theory has a 2(K − 1)-dimensional 'moduli space' of supersymmetric configurations. We argue that in this case the SU(K) gauge symmetry is unbroken everywhere in the 'moduli space' and that this five-dimensional gauge theory is coupled to a four-dimensional theory on the boundary of AdS 5 whose coupling constants depend on the 'moduli'. This involves non-standard boundary conditions for the gauge fields on AdS 5 . Near the origin of the 'moduli space', the theory on the boundary contains a weakly coupled four-dimensional N = 2 supersymmetric SU(K) gauge theory. We show that this implies large corrections to the metric on the 'moduli space'. The embedding in string theory implies that the six-dimensional N = (2, 0) theory on AdS 5 × S 1 with sources on the boundary is a subsector of the large N limit of various four-dimensional N = 2 JHEP03(2015)121quiver SCFTs that remains non-trivial in the large N limit. The same subsector appears universally in many different four-dimensional N = 2 SCFTs. We also discuss a decoupling limit that leads to N = (2, 0) 'little string theories' on AdS 5 × S 1 .

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Section: A Simpler Description Of the Physics On Adsmentioning

confidence: 60%

Rigid holography and six-dimensional N = 2 0 $$ \mathcal{N}=\left(2,0\right) $$ theories on AdS5 × S $$ \mathbb{S} $$ 1

Aharony

Berkooz

Rey

2015

J. High Energ. Phys.

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“…The notion of good, bad and ugly theories was introduced by Gaiotto and Witten [1] in order to classify 3d N = 4 theories according to their expected IR behavior. A bad theory is defined as one for which the IR scaling dimensions of certain BPS monopole operators violate the unitarity bound.…”

Section: Generalities and Summary Of Resultsmentioning

confidence: 99%

“…This suggests that these quivers might constitute a good dual of the bad quiver. 1 We would like to emphasize that the moduli spaces of the bad and the proposed good theory, defined on a flat space-time, are not isomorphic. Instead, there is a special sublocus on the moduli space of the bad theory, where the low energy effective field theory factorizes into an SCFT (U(1) with two flavors with masses and FI parameters tuned to zero) and the Coulomb branch of an SU(2) gauge theory with N flavors.…”

Section: Jhep05(2018)114mentioning

confidence: 99%

Good IR duals of bad quiver theories

Dey

Koroteev

2018

J. High Energ. Phys.

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The infrared dynamics of generic 3d N = 4 bad theories (as per the goodbad-ugly classification of Gaiotto and Witten) are poorly understood. Examples of such theories with a single unitary gauge group and fundamental flavors have been studied recently, and the low energy effective theory around some special point in the Coulomb branch was shown to have a description in terms of a good theory and a certain number of free hypermultiplets. A classification of possible infrared fixed points for bad theories by Bashkirov, based on unitarity constraints and superconformal symmetry, suggest a much richer set of possibilities for the IR behavior, although explicit examples were not known. In this note, we present a specific example of a bad quiver gauge theory which admits a good IR description on a sublocus of its Coulomb branch. The good description, in question, consists of two decoupled quiver gauge theories with no free hypermultiplets.

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“…A fractional level is acceptable for a U(1) gauge theory, but it is in conflict with the level quantization in nonabelian gauge theories. For a recent discussion on this point see [33]. In order to avoid this issue, in the rest of this note we will restrict attention to the special case where n ′ = 1.…”

Section: Jhep11(2008)001mentioning

confidence: 99%

“…This is perfectly consistent for U(1) gauge groups, however, it is inconsistent with the quantization of the level for non-abelian gauge groups. It has been proposed that in this case extra interactions need to be taken into account [32,33].…”

Section: Closing Remarksmentioning

confidence: 99%