Sergio Cecotti

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

We develop techniques to compute higher loop string amplitudes for twistedN=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 theN=2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira-Spencer theory, which may be viewed as the closed string analog of the Chern-Simons 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 correspondingN=2 theory. Relations withc=1 strings are also pointed out.

Geometry of Type II Superstrings and the Moduli of Superconformal Field Theories

We study general properties of the low-energy effective theory for 4D type II superstrings obtained by the compactification on an abstract (2,2) superconformal system. This is the basic step towards the construction of their moduli space. We give an explicit and general algorithm to convert the effective Lagrangian for the type IIA into that of type IIB superstring defined by the same (2,2) superconformal system (and vice versa). This map converts Kahler manifolds into quaternionic ones (and quaternionic into Kahlerian ones) and has a deep geometrical meaning. The relationship with the theory of normal quaternionic manifolds (and algebras), as well as with Jordan algebras, is outlined. It turns out that only a restricted class of quarternionic geometries is allowed in the string case. We derive a general and explicit formula for the (fully nonlinear) couplings of the vector-multiplets (IIA case) in terms of the basic three-point functions of the underlying superconformal theory. A number of illustrative e...

Topological—anti-topological fusion

Abstract We study some non-perturbative aspects of N = 2 supersymmetric quantum field theories (both superconformal and massive deformations thereof). We show that the metric for the supersymmetric ground states, which in the conformal limit is essentially the same as Zamolodchikovs metric, is pseudo-topological and can be viewed as a result of fusion of the topological version of N = 2 theory with its conjugate. For special marginal/relevant deformations (corresponding to theories with factorizable S-matrix), the ground state metric satisfies classical Toda/Affine Toda equations as a function of perturbation parameters. The unique consistent boundary conditions for these differential equations seem to predict the normalized OPE of chiral fields at the conformal point. Also the subset of N = 2 theories whose chiral ring is isomorphic to SU(N)κ Verlinde ring turns out to lead to affine Toda equations of SU(N) type satisfied by the ground state metric.

On classification of N=2 supersymmetric theories

We find a relation between the spectrum of solitons of massive

Higher derivative supergravity is equivalent to standard supergravity coupled to matter

N=2

Supersymmetric born-infeld lagrangians

quantum field theories in

T-branes and monodromy

d=2

Properties of E6 breaking and superstring theory

and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetric

Hidden non-compact symmetries in string theory

N=2

Constraints on partial super-Higgs

conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A--D--E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory.We find a relation between the spectrum of solitons of massiveN=2 quantum field theories ind=2 and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetricN=2 conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A-D-E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory.