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## Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes (1994)

Venue: | Commun. Math. Phys |

Citations: | 539 - 59 self |

### Citations

2094 |
Principles of algebraic geometry
- Griffiths, Harris
- 1994
(Show Context)
Citation Context ...lies that the fermion numbers in this case are not simply identified as the left and right degrees of form, as that would lead to a wrong commutation relation with G + . To fix this, we should recall =-=[11]-=- that for Kähler manifolds there is an sl(2) action on the forms, generated by wedging with the Kähler class k, contracting with k which we represent by k † and the shifted total degree of the form (p... |

292 |
Topological methods in Algebraic Geometry
- Hirzebruch
- 1966
(Show Context)
Citation Context ...Kähler form for the Zamolodchikov metric on moduli space. Therefore we wish to prove the following equation ∫ 2πi M Td(T) n∑ (−1) p=0 p p Ch(∧ n−p T ∗ ) ∣ (1,1)−part We start by recalling a few facts =-=[40]-=-. First of all, Td(T) n∑ p=0 ∣ (−1) p Ch(∧ p T ∗ ) = cn(T) 84 = 1 12 χ(M) G (5.30)(T ∗ is the cotangent bundle). This is (a special case of) theorem 10.1.1 in [40]. Now we apply the Hirzebruch argume... |

256 |
String Field Theory: Quantum Action and
- Zwiebach
- 1993
(Show Context)
Citation Context ...uation in the Tian gauge to write the action giving rise to these equations, or directly use the rules for constructing closed string field theory along general lines discussed in the literature (see =-=[33]-=- for a thorough review of the literature). We will follow the first line and see why it is the same as the second. To write an action we first need to fix some data: the point P (which we sometimes de... |

63 |
Two-dimensional black hole as a topological coset model of c = 1 string theory,” Nucl
- Mukhi, Vafa
- 1993
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Citation Context ... N = 2 topological models are closely related to c = 1 model coupled to gravity. In fact it has been shown that a particular ĉ = 3 twisted N = 2 theory is equivalent to c = 1 model coupled to gravity =-=[50]-=-. To see the logarithmic scaling violation, consider Fg as a function of cosmological constant ∆ which can be identified with 2π(t −α). For large areas (n) one can replace the summation by integral ∫ ... |

49 |
on the Antifield-BRST Formalism for Gauge Theories, Nucl.Phys.B (Proc.Suppl.) 18A
- Henneaux
- 1990
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Citation Context ... and is equal to FL + FR = (p + q − 3). The original KS field A ′ has the ghost number 2. The consistent scheme for quantization string field theory is given by Batalin– Vilkovisky (BV) formalism [35]=-=[36]-=-. In the Batalin-Vilkovisky formalism one has to relax the condition for the ghost numbers of string field and include all possible fields with arbitrary ghost numbers. The fields A with ghost numbers... |

21 |
Quantum Background Independence
- Witten
(Show Context)
Citation Context ...he holomorphic anomaly equations. In Appendix B, we analyse the two equation directly to all order in g. The order-by-order solution of the anomaly equation is presented in section 6. Recently Witten =-=[27]-=- discussed the implication of the holomorphic anomaly, which we had previously announced in [19], to the background (in)dependence of the string theory. There he also derived two equations, one involv... |

15 | Private communications
- Tian
- 2007
(Show Context)
Citation Context ...hich satisfy the gauge condition ∂A ′ = ∂B ′ = 0. It was proven by Tian [29] that [A, B] ′ = ∂(A ∧ B) ′ , (5.6) Later we will need the generalization of Tian’s lemma where A, B belong to Ω p (∧ q TM) =-=[30]-=-. Using this lemma we can rewrite the KS equation in Tian form ¯∂A ′ + 1 2 ∂(A ∧ A)′ = 0. 65The tangent space to the moduli space of complex structures is given by H (0,1) (TM). Let A1 be an infinite... |

6 |
Annals of Math. 67
- Kodaira, Spencer
- 1958
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Citation Context ...of this theory. The complex structure on manifold M is determined by the ¯ ∂ operator. To the first order the change of complex structure is described by deformation of ¯ ∂ operator ¯∂ → ¯ ∂ + A i ∂i =-=[28]-=-. This is a deformation of ¯ ∂ operator acting on functions. One can describe not only the infinitesimal deformations of complex structure but a finite one. The new complex structure is described by r... |

4 |
constructed from matter field in topological Landau-Ginzburg theories coupled to topological gravity
- Losev
(Show Context)
Citation Context ...mplitudes [21]. Thus one would expect an interesting mixture with the anomaly discussed in this paper. In this connection the Landau-Ginzburg formulation of the descendants may be particularly useful =-=[65]-=-. Typically string theories have infinitely many particles. However there are some cases known where string theory has only a finite number of particles. Precisely in these cases the string theory see... |

3 |
in Essays on Mirror manifolds
- Tian
- 1992
(Show Context)
Citation Context ...e clear later that these conditions fix the solution uniquely. Let A, B be vector fields with the coefficients in (0, 1) forms which satisfy the gauge condition ∂A ′ = ∂B ′ = 0. It was proven by Tian =-=[29]-=- that [A, B] ′ = ∂(A ∧ B) ′ , (5.6) Later we will need the generalization of Tian’s lemma where A, B belong to Ω p (∧ q TM) [30]. Using this lemma we can rewrite the KS equation in Tian form ¯∂A ′ + 1... |

2 |
Higher analytic torsion forms for direct images and anomaly formulas, Univ. de Paris-sud, preprint
- Phys
- 1986
(Show Context)
Citation Context ...tegral is regularized by taking s to run from ǫ > 0 to ∞. The main technique to compute the Ray-Singer holomorphic torsion has been recently developed in connection with Quillen’s holomorphic anomaly =-=[38]-=-. Consider a family of complex structures on M parametrized by a complex parameter t. Let us assume that there are no jumps in the zero modes of ∂V . Choose a holomorphic basis for the zero modes of ∂... |

1 |
in Arithmetic and Geometry, papers dedicated to I.R
- Bryant, Griffiths
- 1983
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Citation Context ... tt∗ equations together with the CPT constraint η −1 g = (g −1 ) t η ∗ . Special geometry originally was discovered in two seemingly unrelated contexts: The geometry of periods on a Calabi–Yau 3–fold =-=[13]-=- and N = 2 supergravity in four dimensions [14]. The ground state geometry of ĉ = 3 superconformal theories combines these two topics together in a natural way. In the present paper we shall use quite... |

1 |
Chern–Simons Gauge Theory as a String Theory
- B354
- 1991
(Show Context)
Citation Context ...d in connection with matrix models, one needs to include the full topological gravity multiplet and construct gravitational descendants which give rise to non-vanishing correlation functions [20][21] =-=[22]-=-. Also for ĉ > 3 one needs fractional chiral fields φi with charges between 0 < q < 1 in order to have a chance of balancing the charges (gravitational descendants do not help in this case as they con... |

1 |
Annals of Math 75
- Kuranishi
- 1962
(Show Context)
Citation Context ... Ω0 + A ′ + (A ∧ A) ′ + (A ∧ A ∧ A) ′ . (5.11) Coordinates in H (0,1) (TM), denoted by x, may serve as affine coordinates on some open neighborhood of the moduli space of complex structures (see also =-=[32]-=-) thanks to the Tian’s mapping. These coordinates are in fact very special (not to be confused with special coordinates except for the particular case of base point at infinity, as discussed in sectio... |

1 |
in Arithmetic and Geometry, papers dedicated to I.R
- Mumford
- 1983
(Show Context)
Citation Context ...4) The integrals ∫ Mg c3g−1 , can be easily computed if we know the Chow ring of Mg. In fact, by definition our ck are represented in the Chow ring by the tautological classes λk (notations as in ref.=-=[45]-=-). 33 This is the same situation we encountered in section 2.1 in the context of special geometry in section 2.1. The trivial bundle H plays here the same role as H 3 (M,C) in section 2. 95s6. Solutio... |

1 |
649; S.Ferrara, C.Kounnas, D.Lüst and F.Zwirner, Nucl. Phys. B365
- B307
- 1988
(Show Context)
Citation Context ... In the context of heterotic strings the one–loop contribution to threshold correction for gauge coupling is related to the topological amplitude we have been discussing. In fact it has been shown in =-=[58]-=- that the one–loop corrected gauge coupling constant which depends on the moduli of the internal theory can be written as 16π2 16π = ka (µ) 2 g 2 a g 2 GUT + ba · log M2 GUT µ 2 + ∆a (8.8) where a den... |