Vafa-Witten theory on<i>N</i>= 2 and<i>N</i>= 4 twisted superspace in four dimensions

Kato, Junji; Miyake, Akiko

doi:10.1088/1126-6708/2009/03/087

Cited by 3 publications

(6 citation statements)

References 84 publications

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“…The scalar and the two-form are even and the vector is odd, or the other way around. We show that this is a truncation of a representation of the topologically twisted N = 2 theory given in [11] (see also [12]). Since in this paper we are mainly interested in representations in Minkowski spacetime, we discuss the existence of a similar multiplet in Minkowskian signature.…”

Section: Introductionmentioning

confidence: 82%

“…Inspired by Refs. [11] and [12], we construct a multiplet with the same field content as in the previous section but with a nontrivial action of the central charge operators on the fields. We are interested in multiplets satisfying (2.19).…”

Section: Another Y = 0 Multipletmentioning

confidence: 99%

“…In [11] and [12], an N = 2 twisted superspace formalism with a central charge in fourdimensional Euclidean space is constructed, by introducing a Dirac-Kähler twist. This twist leads to the following supertranslation algebra…”

Section: Y = 1/2 Multiplet and Twisted Topological Modelsmentioning

confidence: 99%

“…We will call this algebra tensor supersymmetry algebra (TSUSY), due to the fact that the extra odd generator present there with respect to VSUSY is an antiselfdual two-form Q + µν . In [11] and [12], multiplets which are a representation of TSUSY are constructed. These are clearly also representations of VSUSY, but as such they are in general not irreducible.…”

Section: Y = 1/2 Multiplet and Twisted Topological Modelsmentioning

confidence: 99%

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Field representations of vector supersymmetry

Casalbuoni

Elmetti

Knapen

et al. 2010

J. High Energ. Phys.

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We study some field representations of vector supersymmetry with superspin Y = 0 and Y = 1/2 and nonvanishing central charges. For Y = 0, we present two multiplets composed of four spinor fields, two even and two odd, and we provide a free action for them. The main differences between these two multiplets are the way the central charge operators act and the compatibility with the Majorana reality condition on the spinors. One of the two is related to a previously studied spinning particle model. For Y = 1/2, we present a multiplet composed of one even scalar, one odd vector and one even selfdual two-form, which is a truncation of a known representation of the tensor supersymmetry algebra in Euclidean spacetime. We discuss its rotation to Minkowski spacetime and provide a set of dynamical equations for it, which are however not derived from a Lagrangian. We develop a superspace formalism for vector supersymmetry with central charges and we derive our multiplets by superspace techniques. Finally, we discuss some representations with vanishing central charges.

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Section: Introductionmentioning

confidence: 82%

Section: Another Y = 0 Multipletmentioning

confidence: 99%

Section: Y = 1/2 Multiplet and Twisted Topological Modelsmentioning

confidence: 99%

Section: Y = 1/2 Multiplet and Twisted Topological Modelsmentioning

confidence: 99%

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Field representations of vector supersymmetry

Casalbuoni

Elmetti

Knapen

et al. 2010

J. High Energ. Phys.

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“…We would rename SU (2) B as SU (2) R in this section. This twisted SYM theory is called A-model or Vafa-Witten theory [24][25][26][27]. The theory possesses twisted supersymmetries whose generators are not spinors but scalars, vectors and tensors.…”

Section: Introductionmentioning

confidence: 99%

Mass deformation of twisted super Yang-Mills theory with fuzzy sphere solution

Kato

Kondo

Miyake

2011

J. High Energ. Phys.

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We investigate mass deformation of twisted superalgebra of U (N ) super Yang-Mills (SYM) theories in several models and in several dimensions, motivated by the method formulated in [1]. We show that there are several ways to perform the deformation, if a model possesses four scalar supercharges except for two dimensional B-model. We also evaluate classical vacuum solutions of the potentials of scalar fields for each model. We then find that it is always possible to find fuzzy sphere solution in the theories.

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Formulation of supersymmetry on a lattice as a representation of a deformed superalgebra

2010

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The lattice superalgebra of the link approach is shown to satisfy a Hopf algebraic supersymmetry where the difference operator is introduced as a momentum operator. The breakdown of the Leibniz rule for the lattice difference operator is accommodated as a coproduct operation of (quasi)triangular Hopf algebra and the associated field theory is consistently defined as a braided quantum field theory. Algebraic formulation of path integral is perturbatively defined and Ward-Takahashi identity can be derived on the lattice. The claimed inconsistency of the link approach leading to the ordering ambiguity for a product of fields is solved by introducing an almost trivial braiding structure corresponding to the triangular structure of the Hopf algebraic superalgebra. This could be seen as a generalization of spin and statistics relation on the lattice. From the consistency of this braiding structure of fields a grading nature for the momentum operator is required. *

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Vafa-Witten theory onN= 2 andN= 4 twisted superspace in four dimensions

Cited by 3 publications

References 84 publications

Field representations of vector supersymmetry

Field representations of vector supersymmetry

Mass deformation of twisted super Yang-Mills theory with fuzzy sphere solution

Formulation of supersymmetry on a lattice as a representation of a deformed superalgebra

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