NT=4 equivariant extension of the 3D topological model of Blau and Thompson

Geyer, B.; Mülsch, D.

doi:10.1016/s0550-3213(01)00461-8

Cited by 17 publications

(36 citation statements)

References 36 publications

(70 reference statements)

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“…In four dimensions, the twist of N = 4 is introduced by Marcus [6]. The three dimensional N = 4 and N = 8 and two dimensional N = (8,8), N = (4, 4) theories are presented by Blau and Thompson [7] and are examined in more detail in [33,34]. The twist of the two dimensional N = (2, 2) theory seems to be a new example of [6,7] type and is examined in more detail here.…”

Section: Introductionmentioning

confidence: 99%

Twisted supersymmetric gauge theories and orbifold lattices

Ünsal

2006

J. High Energy Phys.

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We examine the relation between twisted versions of the extended supersymmetric gauge theories and supersymmetric orbifold lattices. In particular, for the N = 4 SYM in d = 4, we show that the continuum limit of orbifold lattice reproduces the twist introduced by Marcus, and the examples at lower dimensions are usually Blau-Thompson type. The orbifold lattice point group symmetry is a subgroup of the twisted Lorentz group, and the exact supersymmetry of the lattice is indeed the nilpotent scalar supersymmetry of the twisted versions. We also introduce twisting in terms of spin groups of finite point subgroups of R-symmetry and spacetime symmetry.

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Section: Introductionmentioning

confidence: 99%

Twisted supersymmetric gauge theories and orbifold lattices

Ünsal

2006

J. High Energy Phys.

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“…A gauge invariant andQ-invariant action may be taken as (following [4]) 5) where F (a) = da + a 2 is the curvature of the Yang-Mills connection a and * is the Hodge duality operator (see appendix A). One sees that the Lagrange multiplier 0 b 2 implements the zero-curvature condition F (a) = 0 -or the selfduality condition, as in the original Witten's paper.…”

Section: Transformation Rules and Invariant Actionsmentioning

confidence: 99%

“…They are completely symmetric in their indices since, the coordinates θ being anti-commutative, the differentials dθ I are commutative. The superspace exterior derivative is defined asd 5) and is nilpotent:…”

Section: N T Superspace Formalismmentioning

confidence: 99%

“…5 Recall that the indices p and s in s ϕ g p respectively denote the form degree and the SUSY-number. The indice g denotes the ghost number associated to the BRST invariance defined by (3.9) -or (2.2), in the WZ gauge.…”

Section: The Geometrical Sectormentioning

confidence: 99%

“…The result is rather cumbersome and redundant, but the authors of [4] succeeded to construct a reduced procedure with a minimum number of fields. The reduced procedure amounts to introduce a set of superfields, which we shall denote by 5) and to add to the action (4.2) the terms…”

Section: The Blau-thompson Gauge Fixingmentioning

confidence: 99%

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Superspace gauge fixing of topological Yang-Mills theories

2004

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We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of "shift supersymmetry" generators, using a superspace formalism. The super-BF structure of these theories is exploited in order to determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and BF gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type.

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An $$ \mathcal{N}=1 $$ 3d-3d correspondence

Eckhard

Schäfer‐Nameki

Wong

2018

J. High Energ. Phys.

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M5-branes on an associative three-cycle M 3 in a G 2 -holonomy manifold give rise to a 3d N = 1 supersymmetric gauge theory, T N =1 [M 3 ]. We propose an N = 1 3d-3d correspondence, based on two observables of these theories: the Witten index and the S 3 -partition function. The Witten index of a 3d N = 1 theory T N =1 [M 3 ] is shown to be computed in terms of the partition function of a topological field theory, a super-BFmodel coupled to a spinorial hypermultiplet (BFH), on M 3 . The BFH-model localizes on solutions to a generalized set of 3d Seiberg-Witten equations on M 3 . Evidence to support this correspondence is provided in the abelian case, as well as in terms of a direct derivation of the topological field theory by twisted dimensional reduction of the 6d (2, 0) theory. We also consider a correspondence for the S 3 -partition function of the T N =1 [M 3 ] theories, by determining the dimensional reduction of the M5-brane theory on S 3 . The resulting topological theory is Chern-Simons-Dirac theory, for a gauge field and a twisted harmonic spinor on M 3 , whose equations of motion are the generalized 3d Seiberg-Witten equations. For generic G 2 -manifolds the theory reduces to real Chern-Simons theory, in which case we conjecture that the S 3 -partition function of T N =1 [M 3 ] is given by the Witten-ReshetikhinTuraev invariant of M 3 .

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NT=4 equivariant extension of the 3D topological model of Blau and Thompson

Cited by 17 publications

References 36 publications

Twisted supersymmetric gauge theories and orbifold lattices

Twisted supersymmetric gauge theories and orbifold lattices

Superspace gauge fixing of topological Yang-Mills theories

An $$ \mathcal{N}=1 $$ 3d-3d correspondence

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