Improved methods for hypergraphs

Jain, Dharmesh; Siegel, Warren

doi:10.1103/physrevd.88.025018

Cited by 9 publications

(16 citation statements)

References 32 publications

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“…in order to do the power counting. For that the naive real superspace R 4|8 that we use here might be way too complicated [39] and one should maybe instead turn to the N = 2 Harmonic [47] or Projective [44,54,55] superspace formalism.…”

Section: A Non-renormalization Theoremmentioning

confidence: 98%

“…What is more, background field formalism makes gauge invariance manifest and when combined with supersymmetry leads to very powerful non-renormalization theorems that explain many "miraculous cancellations" 10 [35][36][37][38][39][40][41]. For a more modern approach on the background field method (BFM) in N = 2 superspace the interested reader can see [42,43] for Harmonic and [44] for Projective superspace.…”

Section: Languagementioning

confidence: 99%

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Integrability inN=2superconformal gauge theories

Pomoni

2015

Nuclear Physics B

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Any N=2 superconformal gauge theory (including N=4 SYM) contains a set of local operators made only out of fields in the N=2 vector multiplet that is closed under renormalization to all loops, namely the SU(2,1|2) sector. For planar N=4 SYM the spectrum of local operators can be obtained by mapping the problem to an integrable model (a spin chain in perturbation theory), in principle for any value of the coupling constant. We present a diagrammatic argument that for any planar N=2 superconformal gauge theory the SU(2,1|2) Hamiltonian acting on infinite spin chains is identical to all loops to that of N=4 SYM, up to a redefinition of the coupling constant. Thus, this sector is integrable and anomalous dimensions can be, in principle, read off from the N=4 ones up to this redefinition.Comment: 42 pages, 33 figure

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Section: A Non-renormalization Theoremmentioning

confidence: 98%

Section: Languagementioning

confidence: 99%

Integrability inN=2superconformal gauge theories

Pomoni

2015

Nuclear Physics B

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“…For simplicity, we present only the Yang Mills part of the theory, but the procedure carries over to quarks and also to supersymmetric N = 1 and N = 2 theories in the appropriate superspace [27][28][29][30].…”

Section: The Diagrammatic Argument and The Power Of Gauge Invariancementioning

confidence: 99%

Exact effective couplings of four dimensional gauge theories withN=2supersymmetry

Mitev

Pomoni

2015

Phys. Rev. D

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The anomalous dimensions of operators in the purely gluonic SU(2,1|2) sector of any planar conformal N = 2 theory can be read off from the N = 4 SYM results by replacing the N = 4 coupling constant by an interpolating function of the N = 2 coupling constants [1], to which we refer to as the effective coupling. For a large class of N = 2 theories we compute the weak coupling expansion of these functions as well as the leading strong coupling term by employing supersymmetric localization. Via Feynman diagrams, we interpret our results as the relative (between N = 2 and N = 4) finite renormalization of the coupling constant. Using the AdS/CFT dictionary, we identify the effective couplings with the effective string tensions of the corresponding gravity dual theories. Thus, any observable in the SU(2,1|2) sector can be obtained from its N = 4 counterpart by replacing the N = 4 coupling constant by the universal, for a given theory, effective coupling.

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“…In these cases, the Killing potential may be chosen in special form D ++ r = − 1 2 Q + a J a+ r . 17 When the Lagrangian is superconformal, this is always possible. By taking (6.16) and replacing one δ with a gauge transformation and the other with a dilatation, one may find the special form of the moment map on a hyperkähler cone,…”

Section: Jhep03(2016)107mentioning

confidence: 99%

“…This expression also follows by replacing the variations in (6.16) with D 0 v and D −− v : in other words, the function K is a component of the pullback of Ω ++ to the complex harmonic manifold. 17 This choice for the Killing potential is actually always possible provided we do not adopt the special gauge L + a = Q + a . As is familiar from Kähler target spaces in N = 1 theories [64], it is possible to introduce non-dynamical multiplets with vanishing kinetic terms whose sole purpose is to render the Lagrangian completely gauge invariant, so that minimal substitution may proceed.…”

Section: Jhep03(2016)107mentioning

confidence: 99%

On conformal supergravity and harmonic superspace

Butter

2016

J. High Energ. Phys.

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This paper describes a fully covariant approach to harmonic superspace. It is based on the conformal superspace description of conformal supergravity and involves extending the supermanifold M 4|8 by the tangent bundle of CP 1 . The resulting superspace M 4|8 × T CP 1 can be identified in a certain gauge with the conventional harmonic superspace M 4|8 × S 2 . This approach not only makes the connection to projective superspace transparent, but simplifies calculations in harmonic superspace significantly by eliminating the need to deal directly with supergravity prepotentials. As an application of the covariant approach, we derive from harmonic superspace the full component action for the sigma model of a hyperkähler cone coupled to conformal supergravity. Further applications are also sketched.

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Improved methods for hypergraphs

Cited by 9 publications

References 32 publications

Integrability inN=2superconformal gauge theories

Integrability inN=2superconformal gauge theories

Exact effective couplings of four dimensional gauge theories withN=2supersymmetry

On conformal supergravity and harmonic superspace

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