Finiteness of 2D topological BF-theory with matter coupling

Leitgeb, R.; Schweda, M.; Zerrouki, H.

doi:10.1016/s0550-3213(98)00778-0

Cited by 12 publications

(21 citation statements)

References 13 publications

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“…Using the operators {D ± I } defined in (4.17), we may impose two types of chiral conditions. The first type is given as follows: 26) which are essentially equivalent to the previous chiral conditions (3.56) and (3.66), respectively. Here we propose to impose other type of chiral conditions…”

Section: Vector Superfield and Gauge Symmetry For N = 4 Twisted Susy mentioning

confidence: 99%

“…It was later stressed that a (pseudo) scalar SUSY was also accompanied together with BRST and vector SUSY [21]. Then there appeared many related works [22][23][24][25][26][27][28][29][30] [ [31][32][33][34]. The connection of the extended SUSY and the quantization procedure of anti-field formalism by Batalin and Vilkovisky was also investigated [35,36].…”

Section: Introductionmentioning

confidence: 99%

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N=4 twisted superspace from Dirac–Kähler twist and off-shell SUSY invariant actions in four dimensions

2005

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We propose N = 4 twisted superspace formalism in four dimensions by introducing Dirac-Kähler twist. In addition to the BRST charge as a scalar counter part of twisted supercharge we find vector and tensor twisted supercharges. By introducing twisted chiral superfield we explicitly construct off-shell twisted N = 4 SUSY invariant action. We can propose variety of supergauge invariant actions by introducing twisted vector superfield. We may, however, need to find further constraints to identify twisted N = 4 super Yang-Mills action. We propose a superconnection formalism of twisted superspace where constraints play a crucial role. It turns out that N = 4 superalgebra of Dirac-Kähler twist can be decomposed into N = 2 sectors. We can then construct twisted N = 2 super Yang-Mills actions by the superconnection formalism of twisted superspace in two and four dimensions.

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Section: Vector Superfield and Gauge Symmetry For N = 4 Twisted Susy mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

N=4 twisted superspace from Dirac–Kähler twist and off-shell SUSY invariant actions in four dimensions

2005

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“…This action has not only the BRST symmetry (2.9), but also has two more fermionic symmetries [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] as shown in the following table 1. We can see that these operators …”

Section: N=d=2 Super Bf From Quantized Bf Theorymentioning

confidence: 99%

Twisted Superspace for N=d=2 Super Bf and Yang–mills With Dirac–kähler Fermion Mechanism

Kato

Kawamoto

Uchida

2004

Int. J. Mod. Phys. A

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We propose a twisted D=N=2 superspace formalism. The relation between the twisted super charges including the BRST charge, vector and pseudo scalar super charges and the N=2 spinor super charges is established. We claim that this relation is essentially related with the Dirac-Kähler fermion mechanism. We show that a fermionic bilinear form of twisted N=2 chiral and anti-chiral superfields is equivalent to the quantized version of BF theory with the Landau type gauge fixing while a bosonic bilinear form leads to the N=2 Wess-Zumino action. We then construct a Yang-Mills action described by the twisted N=2 chiral and vector superfields, and show that the action is equivalent to the twisted version of the D=N=2 super Yang-Mills action, previously obtained from the quantized generalized topological Yang-Mills action with instanton gauge fixing.

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“…The BF-models have been widely investigated since the middle of the eighties [1][2][3][4][5][6][7][8][9][10][11][12], specially the two-dimensional BF-model in connection with topological quantum gravity [1][2][3][4]. The properties of ultraviolet and infrared perturbative finiteness of the two-dimensional BF-model have been rigorously proved in the framework of algebraic renormalization [5], there the authors make use of an additional symmetry peculiar to topological models in the Landau gauge, called vector-supersymmetry [6,[13][14][15].…”

mentioning

confidence: 99%

“…As a natural extension of the two-dimensional case, it has been proposed in [3] an extended BF-model, as a gauge theory for topological quantum gravity, which accommodates a topological matter coupling. Later, the authors of [7] have been shown that the model proposed in [3] is still ultraviolet and infrared finite at all orders in perturbation theory by using the same approach as those of [5] have done to the pure two-dimensional BF-model.…”

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confidence: 99%

On the finiteness of a new topological model in D=3

1999

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A new topological model is proposed in three dimensions as an extension of the BF-model. It is a three-dimensional counterpart of the two-dimensional model introduced by Chamseddine and Wyler ten years ago. The BFK-model, as we shall call it, shows to be quantum scale invariant at all orders in perturbation theory. The proof of its full finiteness is given in the framework of algebraic renormalization.

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Finiteness of 2D topological BF-theory with matter coupling

Cited by 12 publications

References 13 publications

N=4 twisted superspace from Dirac–Kähler twist and off-shell SUSY invariant actions in four dimensions

N=4 twisted superspace from Dirac–Kähler twist and off-shell SUSY invariant actions in four dimensions

Twisted Superspace for N=d=2 Super Bf and Yang–mills With Dirac–kähler Fermion Mechanism

On the finiteness of a new topological model in D=3

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