N=2 Superconformal Models as Topological Field Theories

Eguchi, Tohru; Yang, Sung–Kil

doi:10.1142/s0217732390001943

Cited by 238 publications

(282 citation statements)

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“…In this section, we show that our effective supercurrents in (3.16) forms a topological conformal algebra [13,22], which appears in two-dimensional topological (conformal) field theories [10,11]. This observation was reported in our previous communication [12].…”

Section: Brst Supercurrent Algebra and The Topological Conformal Algebrasupporting

confidence: 77%

Covariant currents in N = 2 super-Liouville theory

Gomis

Suzuki

1993

Nuclear Physics B

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Based on a path integral prescription for anomaly calculation, we analyze an effective theory of the two-dimensional N = 2 supergravity, i.e., N = 2 superLiouville theory. We calculate the anomalies associated with the BRST supercurrent and the ghost number supercurrent. From those expressions of anomalies, we construct covariant BRST and ghost number supercurrents in the effective theory.We then show that the (super-)coordinate BRST current algebra forms a superfield extension of the topological conformal algebra for an arbitrary type of conformal matter or, in terms of the string theory, for an arbitrary number of space-time dimensions. This fact is very contrast with N = 0 and N = 1 (super-)Liouville theory, where the topological algebra singles out a particular value of dimensions.Our observation suggests a topological nature of the two-dimensional N = 2 supergravity as a quantum theory. * Electronic address: quim@ebubecm1.bitnet † JSPS Junior Scientist Fellow. Also

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Section: Brst Supercurrent Algebra and The Topological Conformal Algebrasupporting

confidence: 77%

Covariant currents in N = 2 super-Liouville theory

Gomis

Suzuki

1993

Nuclear Physics B

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“…In two dimensional topological theories, the same phenomenon is represented by the appearance of a charge at infinity after the twist [5]. We think that the new features of ghost number conservation that appear in twisted N=2 supergravity deserve further investigation.…”

Section: Topological Twist Of N=2 Supergravitymentioning

confidence: 81%

“…After explicit substitution and separation of the various (f, g)-parts, one can read the descent equations 5) where the trace refers to the Lorentz indices. So, we have the following observables 6) where M is the four dimensional manifold where the theory is defined, and γ, S, and V are generic one-, two-and three-dimensional cycles on M. So we have proved that tr[η 0 2 ] corresponds to the Pontriagin number.…”

Section: Topological Gravitymentioning

confidence: 99%

“…By means of bilinear terms it is also possible to define the antighosts ψ 0 ab and ψ 0 , at least up to interaction pieces. The bilinear terms corresponding to them arec A ∧ σ ab 1−γ 5 2 ψ B ǫ AB andc A ∧ ψ B ǫ AB . The above identifications permit to get explicitly the observables of the twisted theory, by simply taking the definitions (3.6), rewriting them in the twisted notation and shifting the gost C. All that is needed is χ 0 ab and η 0 ab , which are given by…”

Section: Matching Between Twisted N=2 Supergravity and Topologicalmentioning

confidence: 99%

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Twisted N = 2 supergravity as topological gravity in four dimensions

1993

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We show that the BRST quantum version of pure D=4 N=2 supergravity can be topologically twisted, to yield a formulation of topological gravity in four dimensions.The topological BRST complex is just a rearrangement of the old BRST complex, that partly modifies the role of physical and ghost fields: indeed, the new ghost number turns out to be the sum of the old ghost number plus the internal U(1) charge. Furthermore, the action of N=2 supergravity is retrieved from topological gravity by choosing a gauge fixing that reduces the space of physical states to the space of gravitational instanton configurations, namely to self-dual spin connections.The descent equations relating the topological observables are explicitly exhibited and discussed. Ours is a first step in a programme that aims at finding the topological sector of matter coupled N=2 supergravity, viewed as the effective Lagrangian of type II superstrings and, as such, already related to 2D topological field-theories. As it stands the theory we discuss may prove useful in describing gravitational instantons moduli-spaces.

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“…We further show that every TFT can be obtained by perturbation from what will be called the standard topological field theory (STFT). As a simple example, the twisted N = 2 minimal topological matters [8] are considered, and shown to live on the boundary of the moduli space of TFT's. Section 7 is devoted to the discussion about how to incorporate gravity into our lattice formulation.…”

Section: Ansatz 1 the Partition Function Of Ltft Which Is First Consmentioning

confidence: 99%

Lattice topological field theory in two dimensions

1994

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The lattice definition of a two-dimensional topological field theory (TFT) is given generically, and the exact solution is obtained explicitly. In particular, the set of all lattice topological field theories is shown to be in one-to-one correspondence with the set of all associative algebras R, and the physical Hilbert space is identified with the center Z(R) of the associative algebra R. Perturbations of TFT's are also considered in this approach, showing that the form of topological perturbations is automatically determined, and that all TFT's are obtained from one TFT by such perturbations. Several examples are presented, including twisted N = 2 minimal topological matter and the case where R is a group ring. *

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N=2 Superconformal Models as Topological Field Theories

Cited by 238 publications

References 0 publications

Covariant currents in N = 2 super-Liouville theory

Covariant currents in N = 2 super-Liouville theory

Twisted N = 2 supergravity as topological gravity in four dimensions

Lattice topological field theory in two dimensions

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