[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

We analyse the Weak Gravity Conjecture for chiral four-dimensional F-theory compactifications with N = 1 supersymmetry. Extending our previous work on nearly tensionless heterotic strings in six dimensions, we show that under certain assumptions a tower of asymptotically massless states arises in the limit of vanishing coupling of a U(1) gauge symmetry coupled to gravity. This tower contains super-extremal states whose charge-to-mass ratios are larger than those of certain extremal dilatonic Reissner-Nordstrom black holes, precisely as required by the Weak Gravity Conjecture. Unlike in six dimensions, the tower of super-extremal states does not always populate a charge sub-lattice. The main tool for our analysis is the elliptic genus of the emergent heterotic string in the chiral N = 1 supersymmetric effective theories. This also governs situations where the heterotic string is non-perturbative. We show how it can be computed in terms of BPS invariants on elliptic four-folds, by making use of various dualities and mirror symmetry. Compared to six dimensions, the geometry of the relevant elliptically fibered four-folds is substantially richer than that of the three-folds, and we classify the possibilities for obtaining critical, nearly tensionless heterotic strings. We find that the (quasi-)modular properties of the elliptic genus crucially depend on the choice of flux background. Our general results are illustrated in a detailed example.

/pdf/modular-fluxes-elliptic-genera-and-weak-gravity-conjectures-579pez68nm.pdf

Modular fluxes, elliptic genera, and weak gravity conjectures in four dimensions

We give a systematic derivation of the consistency conditions which constrain open-closed disk amplitudes of topological strings. They include the A∞ relations (which generalize associativity of the boundary product of topological field theory), as well as certain homotopy versions of bulk-boundary crossing symmetry and Cardy constraint. We discuss integrability of amplitudes with respect to bulk and boundary deformations, and write down the analogs of WDVV equations for the space-time superpotential. We also study the structure of these equations from a string field theory point of view. As an application, we determine the effective superpotential for certain families of D-branes in B-twisted topological minimal models, as a function of both closed and open string moduli. This provides an exact description of tachyon condensation in such models, which allows one to determine the truncation of the open string spectrum in a simple manner.

/pdf/superpotentials-a-relations-and-wdvv-equations-for-open-41isunsnww.pdf

Superpotentials, A ∞ Relations and WDVV Equations for Open Topological Strings

As a refinement of the Swampland Distance Conjecture, we propose that a quantum gravitational theory in an infinite distance limit of its moduli space either decompactifies, or reduces to an asymptotically tensionless, weakly coupled string theory. We support our claim by classifying, as special cases, the behaviour of M-Theory and Type IIA string theory compactifications on Calabi-Yau three-folds at infinite distances in Kahler moduli space. The analysis comprises three parts: We first classify the possible infinite distance limits in the classical Kahler moduli space of a Calabi-Yau three-fold. Each such limit at finite volume is characterized by a universal fibration structure, for which the generic fiber shrinking in the limit is either an elliptic curve, a K3 surface, or an Abelian surface. In the second part we focus on M-Theory and investigate the nature of the towers of asymptotically massless states that arise from branes wrapped on the shrinking fibers. Depending on which of the three classes of fibrations are considered, we obtain decompactification to F-Theory, or a theory with a unique asymptotically tensionless, weakly coupled heterotic or Type II string, respectively. The latter probes a dual D-manifold which is in general non-geometric. In addition to the intrinsic string excitations, towers of states from M2-branes along non-contractible curves become light and correspond to further wrapping and winding modes of the tensionless heterotic or Type II string. In the third part of the analysis, we consider Type IIA string theory on Calabi-Yau three-folds and show that quantum effects obstruct taking finite volume infinite distance limits in the Kahler moduli space. The only possible infinite distance limit which is not a decompactification limit involves K3-fibrations with string scale fiber volume and gives rise to an emergent tensionless heterotic string.

Emergent Strings from Infinite Distance Limits

It is shown how our previous work on lattice constructions of ten-dimensional heterotic strings can be applied to four dimensions. The construction is based on an extension of Narain's lattices by including the bosonized world-sheet fermions and ghosts, and uses conformal field theory as its starting point. A natural embedding of all these theories in the bosonic string is automatically provided. Large numbers of chiral string theories with and without N = 1 supersymmetry can be constructed. Many features of their spectra have a simple interpretation in terms of properties of even self-dual lattices. In particular we find an intriguing relation between extended supersymmetry and exceptional groups.

/pdf/chiral-four-dimensional-heterotic-strings-from-self-dual-3ov3sqg0qy.pdf

Wolfgang Lerche

Papers

Modular fluxes, elliptic genera, and weak gravity conjectures in four dimensions

Superpotentials, A ∞ Relations and WDVV Equations for Open Topological Strings

Emergent Strings from Infinite Distance Limits

Chiral Four-Dimensional Heterotic Strings from Self-Dual Lattices

Elliptic index and superstring effective actions