Gauge fields and interactions in matrix string theory

It is shown that all possible N sheeted coverings of the cylinder are contained in type IIA matrix string theory as non-trivial gauge field configurations. Using these gauge field configurations as backgrounds the large N limit is shown to lead to the type IIA conformal field theory defined on the corresponding Riemann surfaces. The sum over string diagrams is identified as the sum over non-trivial gauge backgrounds of the SYM theory.     

Diagrammar and metamorphosis of coset symmetries in dimensionally reduced type IIB supergravity

Studying the reduction of type IIB supergravity from ten to three spacetime dimensions, we describe the metamorphosis of the Dynkin diagram for gravity line “caterpillar” into a type IIB supergravity “ dragonfly” that is triggered by the inclusion of scalars and antisymmetric tensor fields. The final diagram corresponds to type IIB string theory E₈ global symmetry group, which is the subgroup of the conjectured E₁₁ hidden symmetry group. Application of the results for getting the type IIA/IIB T-duality rules and for searching for type IIB vacua solutions is considered.     

Classification of heterotic Pati–Salam models

We extend the classification of free fermionic heterotic-string models to vacua in which the SO(10)$\mathit{SO}(10)$ GUT symmetry is broken at the string level to the Pati–Salam subgroup. Using our classification method we recently presented the first example of a quasi-realistic heterotic-string vacuum that is free of massless exotic states. Within this method we are able to derive algebraic expressions for the Generalised GSO (GGSO) projections for all sectors that appear in the models. This facilitates the programming of the entire spectrum analysis in a computer code. The total number of vacua in the class of models that we classify is ²⁵¹∼¹⁰¹⁵$2^{51}\sim {10}^{15}$. We perform a statistical sampling in this space of models and extract 10¹¹ GGSO configurations with Pati–Salam gauge group. Our results demonstrate that one in every 10⁶ vacua correspond to a three generation exophobic model with the required Higgs states, needed to induce spontaneous breaking to the Standard Model.     

The string landscape: On formulas for counting vacua

We derive formulas for counting certain classes of vacua in the string/M theory landscape. We do so in the context of the moduli space of M-theory compactifications on singular manifolds with _G2$G_2$ holonomy. Particularly, we count the numbers of gauge theories with different gauge groups but equal numbers of U(1)$U(1)$ factors which are dual to each other. The vacua correspond to various symmetry breaking patterns of grand unified theories. Counting these dual vacua is equivalent to counting the number of conjugacy classes of elements of finite order inside Lie groups. We also point out certain cases where the conventional expectation is that symmetry breaking patterns by Wilson lines and Higgs fields are the same, but we show they are in fact different.     

On the string interpretation of M(atrix) theory

It has been proposed recently that, in the framework of M(atrix) theory, = 8 supersymmetric U(N) Yang-Mills theory in 1 + 1 dimensions gives rise to type IIA long string configurations. We point out that the quantum moduli space of SYM_{1 + 1} gives rise to two quantum numbers, which fit very well into the M(atrix) theory. The two quantum numbers become familiar if one switches to a IIB picture, where they represent configurations of D-strings and fundamental strings. We argue that, due to the SL(2,Z) symmetry, of the IIB theory, such quantum numbers must represent configurations that are present also in the IIA framework.     

Representation theory of three-dimensional Sklyanin algebras

We determine the dimensions of the irreducible representations of the Sklyanin algebras with global dimension 3. This contributes to the study of marginal deformations of the N=4$N=4$ super Yang–Mills theory in four dimensions in supersymmetric string theory. Namely, the classification of such representations is equivalent to determining the vacua of the aforementioned deformed theories.     

Flux vacua statistics for two‐parameter Calabi‐Yau's

We study the number of flux vacua for type IIB string theory on an orientifold of the Calabi‐Yau expressed as a hypersurface in WCP ⁴[1,1,2,2,6] by evaluating a suitable integral over the complex‐structure moduli space as per the conjecture of Douglas and Ashok. We show that away from the singular conifold locus, one gets a power law, and that the (neighborhood) of the conifold locus indeed acts as an attractor in the (complex structure) moduli space. In the process, we evaluate the periods near the conifold locus. We also study (non)supersymmetric solutions near the conifold locus, and show that supersymmetric solutions near the conifold locus do not support fluxes.     

Dynamical SUSY breaking in heterotic M-theory

It is shown that four-dimensional N=1$N=1$ supersymmetric QCD with massive flavors in the fundamental representation of the gauge group can be realized in the hidden sector of E₈×E₈$E_8\times E_8$ heterotic string vacua. The number of flavors can be chosen to lie in the range of validity of the free-magnetic dual, using which one can demonstrate the existence of long-lived meta-stable non-supersymmetric vacua. This is shown explicitly for the gauge group Spin(10)$\mathit{Spin}(10)$, but the methods are applicable to Spin(Nc)$\mathit{Spin}(N_c)$, SU(Nc)$\mathit{SU}(N_c)$ and Sp(Nc)$\mathit{Sp}(N_c)$ for a wide range of color index Nc$N_c$. Hidden sectors of this type can potentially be used as a mechanism to break supersymmetry within the context of heterotic M-theory.     

Semi-classical dynamical triangulations

For non-critical string theory the partition function reduces to an integral over moduli space after integrating over matter fields. The moduli integrand is known analytically for genus one surfaces. The formalism of dynamical triangulations provides us with a regularization of non-critical string theory and we show that even for very small triangulations it reproduces very well the continuum integrand when the central charge c   of the matter fields is large negative, thus providing a striking example of how the quantum fluctuations of geometry disappear when c→−∞$c\to -\infty$.     

Some properties of the Alday–Maldacena minimum

The Alday–Maldacena solution, relevant to the n=4$n=4$ gluon amplitude in N=4$N=4$ SYM at strong coupling, was recently identified as a minimum of the regularized action in the moduli space of solutions of the AdS₅${\mathit{AdS}}_5$σ  -model equations of motion. Analogous solutions of the Nambu–Goto equations for the n=4$n=4$ case are presented and shown to form (modulo the reparametrization group) an equally large but different moduli space, with the Alday–Maldacena solution at the intersection of the σ  -model and Nambu–Goto moduli spaces. We comment upon the possible form of the regularized action for n=5$n=5$. A function of moduli parameters za$z_a$ is written, whose minimum reproduces the BDDK one-loop five-gluon amplitude. This function may thus be considered as some kind of Legendre transform of the BDDK formula and has its own value independently of the Alday–Maldacena approach.     

Brane orbits

We complete the classification of half-supersymmetric branes in toroidally compactified IIA/IIB string theory in terms of representations of the T-duality group. As a by-product we derive a last wrapping rule for the space-filling branes. We find examples of T-duality representations of branes in lower dimensions, suggested by supergravity, of which none of the component branes follow from the reduction of any brane in ten-dimensional IIA/IIB string theory. We discuss the constraints on the charges of half-supersymmetric branes, determining the corresponding T-duality and U-duality orbits.