Supersymmetric String Vacua Research Articles

Demystifying the Emergence Proposal

We revisit the Emergence Proposal in the vector multiplet moduli space of type IIA N = 2 supersymmetric string vacua in four dimensions, for which the string tree-level prepotential and the string one-loop correction are exactly known via mirror symmetry. We argue that there exists an exact notion of emergence, according to which these four-dimensional couplings can be computed exactly in any asymptotic limit in field space. In such limits, a perturbative quantum gravity theory emerges, whose fundamental degrees of freedom include all complete infinite towers of states with typical mass scale not larger than the species scale. For a decompactification limit, this picture is closely related to and in fact motivated by the computation of Gopakumar-Vafa invariants. In addition, in the same limit our results suggest that the emergent theory will also contain asymptotically tensionless wrapped NS5-branes.

Distributions of extremal black holes in Calabi-Yau compactifications

We study non-supersymmetric extremal black hole excitations of 4d mathcal{N} = 2 supersymmetric string vacua arising from compactification on Calabi-Yau threefolds. The values of the (vector multiplet) moduli at the black hole horizon are governed by the attractor mechanism. This raises natural questions, such as “what is the distribution of attractor points on moduli space?” and “how many attractor black holes are there with horizon area up to a certain size?” We employ tools developed by Denef and Douglas [1] to answer these questions.

The hidden symmetry of the heterotic string

We propose that Borcherds' Fake Monster Lie algebra is a broken symmetry of heterotic string theory compactified on $T^7 \times T^2$. As evidence, we study the fully flavored counting function for BPS instantons contributing to a certain loop amplitude. The result is controlled by $\Phi_{12}$, an automorphic form for $O(2, 26, \mathbb{Z})$. The degeneracies it encodes in its Fourier coefficients are graded dimensions of a second-quantized Fock space for this large symmetry algebra. This construction provides a concrete realization of Harvey and Moore's proposed relationship between Generalized Kac-Moody symmetries and supersymmetric string vacua.

Heterotic strings on homogeneous spaces

AbstractWe construct heterotic string backgrounds corresponding to families of homogeneous spaces as exact conformal field theories. They contain left cosets of compact groups by their maximal tori supported by NS‐NS 2‐forms and gauge field fluxes. We give the general formalism and modular‐invariant partition functions, then we consider some examples such as SU (2)/U (1) ~ S2 (already described in a previous paper) and the SU (3)/U(1)2 flag space. As an application we construct new supersymmetric string vacua with magnetic fluxes and a linear dilaton.

TYPE I ON (GENERALIZED) VOISIN–BORCEA ORBIFOLDS AND NONPERTURBATIVE ORIENTIFOLDS

We consider nonperturbative four-dimensional [Formula: see text] space–time supersymmetric orientifolds corresponding to Type I compactifications on (generalized) Voisin–Borcea orbifolds. Some states in such compactifications arise in "twisted" open string sectors which lack world sheet description in terms of D-branes. Using Type I-heterotic duality as well as the map between Type IIB orientifolds and F theory we are able to obtain the massless spectra of such orientifolds. The four-dimensional compactifications we discuss in this context are examples of chiral [Formula: see text] supersymmetric string vacua which are nonperturbative from both orientifold and heterotic points of view. In particular, they contain both D9- and D5-branes as well as nonperturbative "twisted" open string sector states. We also explain the origins of various inconsistencies arising in such compactifications for certain choices of the gauge bundle.

Non-perturbative orientifolds

We consider non-perturbative six and four dimensional N=1 space-time supersymmetric orientifolds. Some states in such compactifications arise in “twisted” open string sectors which lack world-sheet description in terms of D-branes. Using Type I-heterotic duality we are able to obtain the massless spectra for some of such orientifolds. The four dimensional compactification we discus in this context is an example of a chiral N=1 supersymmetric string vacuum which is non-perturbative in both orientifold and heterotic pictures. In particular, it contains both D9- and D5-branes plus non-perturbative “twisted” open string sector states as well.

Supersymmetric D3 brane action in AdS5× S5

We find the space-time supersymmetric and κ-invariant action for a D3-brane propagating in the AdS 5× S 5 background. As in the previous construction of the fundamental string action in this maximally supersymmetric string vacuum the starting point is the corresponding superalgebra su(2,2|4). We comment on the super Yang-Mills interpretation of the gauge-fixed form of the action.

A three-family SU(6) type I compactification

We construct a four dimensional chiral N=1 space-time supersymmetric Type I vacuum corresponding to a compactification on a toroidal Z 2⊗ Z 2⊗ Z 3 orbifold. Using recent results in four dimensional orientifolds, we argue that this model has a well defined world-sheet description. An interesting feature of this model is that the gauge group contains an SU(6) subgroup with three chiral generations. Moreover, this model contains D5-branes and therefore corresponds to a non-perturbative heterotic vacuum. This is the first example of a consistent chiral N=1 supersymmetric string vacuum which is non-perturbative from the heterotic viewpoint, has a perturbative description in a dual theory, and possesses some phenomenologically interesting characteristics. We also compute the tree-level superpotential in this theory.

Exactly solvable (0,2) supersymmetric string vacua with GUT gauge groups

We present a construction of modular invariant partition functions for heterotic (0, 2) supersymmetric classical string vacua. This generalization of Gepner's construction yields GUT gauge groups E 6, SO(10), SU(5) and SU(3) × SU(2) × U(1) r , respectively. By calculating the massless spectrum of some of these models we find strong indications that they correspond to (0, 2) string vacua discussed recently in the context of CYM/LG phases.

Singular BPS saturated states and enhanced symmetries of four-dimensional N = 4 supersymmetric string vacua

A class of supersymmetric (BPS saturated), static, spherically symmetric solutions of four-dimensional effective N = 4 supersymmetric superstring vacua, which become massless at special points of moduli space, is studied in terms of the fields of the effective heterotic string theory compactified on a six-torus. Those are singular four-dimensional solutions corresponding to O(6,22, Z) orbits of dyonic configurations (with zero axion), whose left-moving as well as right-moving electric and magnetic charges are orthogonal (light-like in the O(6,22, Z) sense), while the O(6,22, Z) norms of both the electric and magnetic charges are negative. Purely electric [or purely magnetic] and dyonic configurations preserve 1 2 and 1 4 of N = 4 supersymmetry, respectively, thus belonging to the vector and the highest spin 3 2 supermultiplets, respectively. Purely electric [or purely magnetic] solutions (along with an infinite tower of SL(2, Z) transformed states) become massless at a point of the corresponding “one-torus”, thus may contribute to the enhancement of non-Abelian gauge symmetry, while dyonic solutions become simultaneously massless at a point of the corresponding two-torus, and thus may in addition contribute to the enhancement of the local supersymmetry there.

STRONG COUPLING AND THE COSMOLOGICAL CONSTANT

The vanishing of the cosmological constant and the absence of a massless dilaton might be explained by a duality between a supersymmetric string vacuum in three dimensions and a nonsupersymmetric string vacuum in four dimensions.

Number of generations in free fermionic string models.

In string theory there seems to be an intimate connection between spacetime and world-sheet physics. Following this line of thought we investigate the family problem in a particular class of string solutions, namely the free fermionic string models. We find that the number of generations $N_g$ is related to the index of the supersymmetry generator of the underlying $N=2$ internal superconformal field theory which is always present in any $N=1$ spacetime supersymmetric string vacuum. We also derive a formula for the index and thus for the number of generations which is sensitive to the boundary condition assignments of the internal fermions and to certain coefficients which determine the weight with which each spin-structure of the model contributes to the one-loop partition function. Finally we apply our formula to several realistic string models in order to derive $N_g$ and we verify our results by constructing explicitly the massless spectrum of these string models.

Landau-Ginzburg string vacua

We classify (2,2) supersymmetric string vacua which are represented as Landau-Ginzburg theories, with a quasihomogeneous potential that has an isolated singularity at the origin. There are at least three thousand distinct models in this class. All vacua of this type lead to Euler numbers lying in the range −960 ⩽ χ ⩽ 960. The Euler characteristics do not pair up completely; hence the space of Landau-Ginzburg ground states is not mirror-symmetric even though it exhibits a high degree of symmetry. We discuss in some detail the relation between Landau-Ginzburg models and Calabi-Yau manifolds and describe a subtlety regarding Landau-Ginzburg potentials with an arbitrary number of fields. We also show that the use of topological identities makes it possible to relate Landau-Ginzburg theories to types of Calabi-Yau manifolds for which the usual Landau-Ginzburg framework does not apply.

Stringy domain walls and target-space modular invariance.

Based on the target-space modular invariance of the nonperturbative superpotential of the four-dimensional {ital N}=1 supersymmetric string vacua, we find topologically stable, stringy domain walls of nontrivial compactification modulus field configurations. They are supersymmetric solutions, thus saturating the Bogomolnyi bound. Their physical implications are discussed.

Gauged supergravity vacua in string theory

We present a first instance of an exact supersymmetric string vacuum in curved space-time. It corresponds to the Freedman-Gibbons electrovac solution to one version of N=4 supergravity, with N=2 space-tme supersymmetry. The conformal theory includes a Wess-Zumino-Witten model on the SU (1,1) group manifold.