Extended N = 2 superconformal structure of gravity and W-gravity coupled to matter

Bershadsky, M.; Lerche, W.; Nemeschansky, Dennis; Warner, Nicholas P.

doi:10.1016/0550-3213(93)90306-a

Cited by 115 publications

(215 citation statements)

References 79 publications

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“…Bosonic string theory is in many ways like a twisted N = 2 theory [16], [17]. It has a scalar supercharge Q BRST = Q + Q, which is the usual BRST operator.…”

Section: Coupling Twisted N = 2 Theory To Gravitymentioning

confidence: 99%

Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes

et al. 1994

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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories withĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of the N = 2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the KodairaSpencer theory, which may be viewed as the closed string analog of the Chern-Simon theory. Using the mirror map this leads to computation of the 'number' of holomorphic curves of higher genus curves in Calabi-Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2 theory. Relations with c = 1 strings are also pointed out. 9/93

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“…Bosonic string theory is in many ways like a twisted N = 2 theory [16], [17]. It has a scalar supercharge Q BRST = Q + Q, which is the usual BRST operator.…”

Section: Coupling Twisted N = 2 Theory To Gravitymentioning

confidence: 99%

Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes

et al. 1994

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“…The sℓ(2|1)-characters then correspond to N = 2 characters in accordance with the relation between the sℓ(2|1) and N = 2 representations [35,36] under the Hamiltonian reduction [37,38,39].…”

Section: 1mentioning

confidence: 99%

Higher-Level Appell Functions, Modular Transformations, and Characters

Semikhatov

Taorimina

Tipunin

2005

Commun. Math. Phys.

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Bore Fe ginu po sluqa ego p tides tileti ABSTRACT. We study modular transformation properties of a class of indefinite theta series involved in characters of infinite-dimensional Lie superalgebras. The level-ℓ Appell functions K ℓ satisfy open quasiperiodicity relations with additive theta-function terms emerging in translating by the "period." Generalizing the well-known interpretation of theta functions as sections of line bundles, the K ℓ function enters the construction of a section of a rank-(ℓ + 1) bundle V ℓ,τ . We evaluate modular transformations of the K ℓ functions and construct the action of an SL(2, Z) subgroup that leaves the section of V ℓ,τ constructed from K ℓ invariant.Modular transformation properties of K ℓ are applied to the affine Lie superalgebra sℓ(2|1) at rational level k > −1 and to the N = 2 super-Virasoro algebra, to derive modular transformations of "admissible" characters, which are not periodic under the spectral flow and cannot therefore be rationally expressed through theta functions. This gives an example where constructing a modular group action involves extensions among representations in a nonrational conformal model.

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“…To completely understand this relation, it is important to construct the modular invariant partition function which satisfy the condition of critical dimension and evaluate the periods of the supersymmetric cycles. This construction is not well understood so far and may be achieved by combining with the Liouville theory or its generalization [44].…”

Section: Summary and Discussionmentioning

confidence: 99%