[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

A BRST operator for non-critical W-strings

We show how certain non-perturbative superpotentials (Σ), which are the two-dimensional analogs of the Seiberg-Witten prepotential in 4d, can be computed via geometric engineering from 4-folds. We analyze an explicit example for which the relevant compact geometry of the 4-fold is given by 1 fibered over 2. In the field theory limit, this gives an effective U(1) gauge theory with N = (2,2) supersymmetry in two dimensions. We find that the analog of the SW curve is a K3 surface, and that the complex FI coupling is given by the modular parameter of this surface. The FI potential itself coincides with the middle period of a meromorphic differential. However, it only shows up in the effective action if a certain 4-flux is switched on, and then supersymmetry appears to be non-perturbatively broken. This can be avoided by tuning the bare FI coupling by hand, in which case the supersymmetric minimum naturally corresponds to a singular K3.

/pdf/fayet-iliopoulos-potentials-from-four-folds-1jsn6nth2i.pdf

Fayet-Iliopoulos potentials from four folds

Boundary fixed points, enhanced gauge symmetry and singular bundles on K3

We show how the Riemann surface $\Sigma$ of $N=2$ Yang-Mills field theory arises in type II string compactifications on Calabi-Yau threefolds. The relevant local geometry is given by fibrations of ALE spaces. The $3$-branes that give rise to BPS multiplets in the string descend to self-dual strings on the Riemann surface, with tension determined by a canonically fixed Seiberg-Witten differential $\lambda$. This gives, effectively, a dual formulation of Yang-Mills theory in which gauge bosons and monopoles are treated on equal footing, and represents the rigid analog of type II-heterotic string duality. The existence of BPS states is essentially reduced to a geodesic problem on the Riemann surface with metric $|\lambda|^2$. This allows us, in particular, to easily determine the spectrum of {\it stable} BPS states in field theory. Moreover, we identify the six-dimensional space $\IR^4\times \Sigma$ as the world-volume of a five-brane and show that BPS states correspond to two-branes ending on this five-brane.

/pdf/self-dual-strings-and-n-2-supersymmetric-field-theory-3nofionh6e.pdf

Self-Dual Strings and N=2 Supersymmetric Field Theory

We investigate B-type topological Landau-Ginzburg theory with one variable, with D2-brane boundary conditions. We find that the allowed brane configurations are determined in terms of the possible factorizations of the superpotential, and compute the corresponding open string chiral rings. These are characterized by bosonic and fermionic generators that satisfy certain relations. Moreover we show that the disk correlators, being continuous functions of deformation parameters, satisfy the topological sewing constraints, thereby proving consistency of the theory. In addition we show that the open string LG model is, in its content, equivalent to a certain triangulated category introduced by Kontsevich, and thus may be viewed as a concrete physical realization of it.

Wolfgang Lerche

Papers

A BRST operator for non-critical W-strings

Fayet-Iliopoulos potentials from four folds

Boundary fixed points, enhanced gauge symmetry and singular bundles on K3

Self-Dual Strings and N=2 Supersymmetric Field Theory

Landau-Ginzburg Realization of Open String TFT