Heterotic string compactification on N = 2 superconformal theories with c = 9

We study (2, 2) compactifications of the heterotic string by tensoring the discrete N = 2 superconformal series. We construct all models with c = 9 that preserve N = 1 spacetime supersymmetry and discuss some of their properties.     

Observations on the moduli space of superconformal field theories

Some aspects of the moduli space of superconformal field theories are discussed. It is helpful to consider the conformal field theory as a background for propagation of strings and to exploit the space-time interpretation. Using this point of view we show that the metric on the moduli space of N = 4 superconformal field theory with c = 6 is locally that of O(20,4)/O(20) × O(4). We also discover some properties of the moduli space of N = 2 superconformal field theories with c = 9. Particular examples of these conformal field theories are sigma models on four- and six-dimensional Calabi-Yau spaces. Therefore, we can use this technique to learn about the moduli space of these spaces. For c = 6 we recover the known moduli space of K₃. Our analysis of the c = 9 system leads to a new coupling in four dimensional supergravity. As a by-product, we prove that gauge couplings cannot depend on the moduli of N = 1 space-time supersymmetric compactifications.     

Compactifications of F-theory on Calabi-Yau threefolds (II)

We continue our study of compactifications of F-theory on Calabi-Yau threefolds. We gain more insight into F-theory duals of heterotic strings and provide a recipe for building F-theory duals for arbitrary heterotic compactifications on elliptically fibered manifolds. As a byproduct we find that string/string duality in six dimensions gets mapped to fiber/base exchange in F-theory. We also construct a number of new N = 1, d = 6 examples of F-theory vacua and study transitions among them. We find that some of these transition points correspond upon further compactification to 4 dimensions to transitions through analogues of Argyres-Douglas points of N = 2 moduli. A key idea in these transitions is the notion of classifying (0,4) fivebranes of heterotic strings.     

The G2 invariant compactifications in eleven-dimensional supergravity

In this article we study the most general compactifications of eleven-dimensional supergravity to four-dimensional anti-de Sitter space, using a seven-dimensional internal compact manifold whose local isometry group contains the exceptional group, G₂. We find that the only such compactifications are the well known ones involving the round seven-sphere. We discuss the implications of this result for conjectured relationship between the eleven-dimensional theory and gauged N = 8 supergravity.     

Exactly solvable string compactifications on manifolds of SU(N) holonomy

A variety of heterotic string compactifications on the K3 surface, manifolds of SU(3) holomony, and higher holomony manifolds, are solved exactly. An example of the quintic hypersurface in CP₄ is worked out in detail. It is conjectured, and demonstrated in part, that any supersymmetric compactification of the heterotic string with an N=2 superconformal theory is equivalent to a compactification on a manifold of SU(N) holonomy, and in particular an arbitrary gluing of the discrete models with c=9 gives a solvable heterotic string compactification on some Calabi-Yau manifold. Calabi-Yau compactifications are seen to be exact vacua of string theory, retaining their topological and geometrical characteristics. Previously unknown enhanced gauge symmetries are found to arise for certain backgrounds.     

Compactification of chiral N = 2, D = 10 supergravity

A general analysis is made for the possible compactifications of chiral N = 2, D = 10 supergravity down to four dimensions.     

Automorphic black holes as probes of extra dimensions

Recent progress in the understanding of the statistical nature of black hole entropy shows that the counting functions in certain classes of models are determined by automorphic forms of higher rank. In this paper we combine these results with Langlands? reciprocity conjecture to view black holes as probes of the geometry of spacetime. This point of view can be applied in any framework leading to automorphic forms, independently of the degree of supersymmetry of the models. In the present work we focus on the class of Chaudhuri-Hockney-Lykken compactifications defined as quotients associated to ZN groups. We show that the black hole entropy of these CHLN models can be derived from elliptic motives, thereby providing the simplest possible geometric building blocks of the Siegel type entropy count.     

Low-energy analysis of M- and F-theories on Calabi-Yau threefolds

We elucidate the interplay between gauge and supersymmetry anomalies in six-dimensional N = 1 supergravity with generalized couplings between tensor and vector multiplets. We derive the structure of the five-dimensional supergravity resulting from the S₁ reduction of these models and give the constraints on Chem-Simons couplings that follow from duality to M-theory compactified on a Calabi-Yau threefold. The duality is supported only on a restricted class of Calabi-Yau threefolds and requires a special type of intersection form. We derive five-dimensional central-charge formulas and briefly discuss the associated phase transitions. Finally, we exhibit connections with F-theory compactifications on Calabi-Yau manifolds that admit elliptic fibrations. This analysis suggests that F-theory unifies type-IIb three-branes and M-theory five-branes.     

M-theory on eight-manifolds

We show that in certain compactifications of M-theory on eight-manifolds to three-dimensional Minkowski space-time the four-form field strength can have a non-vanishing expectation value, while an N = 2 supersymmetry is preserved. For these compactifications a warp factor for the metric has to be taken into account. This warp factor is non-trivial in three space-time dimensions due to Chern-Simons corrections to the fivebrane Bianchi identity. While the original metric on the internal space is not Kahler, it can be conformally transformed to a metric that is Kähler and Ricci flat, so that the internal manifold has SU(4) holonomy.     

Morita equivalence and duality

It was shown by Connes, Douglas, Schwarz [hep-th/9711162] that one can compactify M(atrix) theory on a non-commutative torus To. We prove that compactifications on Morita equivalent tori are in some sense physically equivalent. This statement can be considered as a generalization of non-classical SL(2,$\text{Z}$)N duality conjectured by Connes, Douglas and Schwarz for compactifications on two-dimensional non-commutative tori.     

D0-branes in Gepner models and N = 2 black holes

In this paper D-brane boundary states constructed in Gepner models are used to analyze some aspects of the dynamics of DO-branes in Calabi-Yau compactifications of type II theories to four dimensions. It is shown that the boundary states correspond to BPS objects carrying dyonic charges. By analyzing the couplings to closed string fields a correspondence between the DO-branes and extremal charged black holes in N = 2 supergravity is found.     

Towards low energy physics from the heterotic string

We investigate orbifold compactifications of the heterotic string, addressing in detail their construction, classification and phenomenological potential. We present a strategy to search for models resembling the minimal supersymmetric extension of the standard model (MSSM) in ℤ₆‐II orbifold compactifications. We find several MSSM candidates with the gauge group and the exact spectrum of the MSSM, and supersymmetric vacua below the compactification scale. They also exhibit the following realistic features: R‐parity, seesaw suppressed neutrino masses, and intermediate scale of supersymmetry breakdown. In addition, we find that similar models also exist in other ℤ_N orbifolds and in the SO(32) heterotic theory.     

Black hole attractors and the entropy function in four‐ and five‐dimensional N = 2 supergravity

In this overview of selected aspects of the black hole attractor mechanism, after introducing the necessary foundations, we examine the relationship between two ways to describe the attractor phenomenon in four‐dimensional N = 2 supergravity: the entropy function and the black hole potential. We also exemplify their practical application to finding solutions to the attractor equations for a conifold prepotential. Next we describe an extension of the original definition of the entropy function to a class of rotating black holes in five‐dimensional N = 2 supergravity based on cubic polynomials, exploiting a connection between four‐ and five‐dimensional black holes. This link allows further the derivation of five‐dimensional first‐order differential flow equations governing the profile of the fields from infinity to the event horizon and construction of non‐supersymmetric interpolating solutions in four dimensions by dimensional reduction. Finally, since four‐dimensional extremal black holes in N = 2 supergravity can be viewed as certain two‐dimensional string compactifications with fluxes, we discuss implications of the conifold example in the context of the entropic principle, which postulates as a probability measure on the space of these string compactifications the exponentiated entropy of the corresponding black holes.     

New compactifications of Chiral N = 2, d = 10 supergravity

We present a number of new compactifying solutions of chiral N = 2 ten-dimensional supergravity to five dimensions. Several are of the standard Freund-Rubin type; we give a complete classification of such compactifications for which the internal space M⁵ is a coset manifold. In another type of solution M⁵ is a non-Einstein U(1) bundle over a four-dimensional Kähler space, and the complex three-index field strength is nonvanishing in the internal directions. The latter construction gives a solution with SU(3) symmetry when M⁵ is taken to be a stretched five-sphere.     

Infinite-parameter symmetries and the Higgs effect in gravity-coupled sigma models in D+4 dimensions

We compute the mass spectra of small fluctuations of four-dimensional fields for Kaluza-Klein models in which the compactification from D+4 to 4 (flat) dimensions is induced by the scalar fields of a nonlinear sigma model defined on an S^N or CP^N manifold. The compactifications are stable for all values of N. The fact that the spectra contain no massless vector fields is traced to the absence of a local gauge invariance for the sigma-model action. We introduce a complete basis for the infinite-parameter symmetries that arise from the harmonic analysis of the higher-dimensional dynamical invariances. The spectrum of spin-one and spin-two fields is consistent with the Higgs effect associated with the breaking of the local symmetries corresponding to these generators. The commutation relations of the infinite parameter algebra for the case of CP¹ are also given. The algebra includes the spectrum-generating algebra SO(1,3) of Salam and Strathdee.     

Beta-functions and superstring compactifications

It is shown that quartic curvature modifications to the gravitational effective action derived from superstrings agree on Ricci-flat Kähler backgrounds with a recently-proposed four-loop counterterm in N = 2 Ricci-flat σ-models. These results seem to suggest that Calabi-Yau manifolds may not provide consistent compactifications of the superstring.     

Nonlinear σ-models and their gauging in and out of superspace

We analyze and generalize bosonic nonlinear σ-models and their N = 1,2 supersymmetric extensions in (4 spacetime-dimensional) N = 1 superspace. We give a general construction of nonminimal kinetic terms for gauge fields and of N = 1,2 gauging of isometries on Kähler and hyper-Kähler manifolds. In particular, we study the gauging of noncompact groups. We derive the complete component action and supertrace formula. For N = 2 models, the supertrace always vanishes.     

Flat coordinates,topological Landau-Ginzburg models and the Seiberg-Witten period integrals

We study the Picard-Fuchs differential equations for the Seiberg-Witten period integrals in N = 2 supersymmetric Yang-Mills theory. For A-D-E gauge groups we derive the Picard-Fuchs equations by using the flat coordinates in the A-D-E singularity theory. We then find that these are equivalent to the Gauss-Manin system for two-dimensional A-D-E topological Landau-Ginzburg models and the scaling relation for the Seiberg-Witten differential. This suggests an interesting relationship between four-dimensional N = 2 gauge theories in the Coulomb branch and two-dimensional topological field theories.