[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

http://inspirehep.net/record/499969/files/arXiv:hep-th_9905111.pdf

Large N Field Theories, String Theory and Gravity

Phases of N = 2 theories in two dimensions

A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory

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.

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

Covariant lattices, superconformal invariance and strings

We study D-brane moduli spaces and tachyon condensation in B-type topological minimal models and their massive deformations. We show that any B-type brane is isomorphic with a direct sum of `minimal' branes, and that its moduli space is stratified according to the type of such decompositions. Using the Landau-Ginzburg formulation, we propose a closed formula for the effective deformation potential, defined as the generating function of tree-level open string amplitudes in the presence of D-branes. This provides a direct link to the categorical description, and can be formulated in terms of holomorphic matrix models. We also check that the critical locus of this potential reproduces the D-branes' moduli space as expected from general considerations. Using these tools, we perform a detailed analysis of a few examples, for which we obtain a complete algebro-geometric description of moduli spaces and strata.

D-brane effective action and tachyon condensation in topological minimal models

We review the generalization of the work of Seiberg and Witten on N=2 supersymmetric SU(2) Yang-Mills theory to SU(n) gauge groups. The quantum moduli spaces of the effective low energy theory parametrize a special family of hyperelliptic genus n-1 Riemann surfaces. We discuss the massless spectrum and the monodromies.

On the Monodromies of N=2 Supersymmetric Yang-Mills Theory

https://cds.cern.ch/record/445529/files/0006247.pdf

/D-branes on ALE spaces and the ADE classification of conformal field theories

We review the generalization of the work of Seiberg and Witten on N = 2 supersymmetric SU(2) Yang-Mills theory to SU(n) gauge groups. The quantum moduli spaces of the effective low energy theory parametrize a special family of hyperelliptic genus n−1 Riemann surfaces. We discuss the massless spectrum and the monodromies.

Wolfgang Lerche

Papers

Covariant lattices, superconformal invariance and strings

D-brane effective action and tachyon condensation in topological minimal models

On the Monodromies of N=2 Supersymmetric Yang-Mills Theory

/D-branes on ALE spaces and the ADE classification of conformal field theories

On the monodromies of N=2 supersymmetric Yang-Mills theory