Ori J. Ganor

Small E8 instantons and tensionless non-critical strings

T-duality is used to extract information on an instanton of zero size in the E8 × E8 heterotic string. We discuss the possibility of the appearance of a tensionless anti-self-dual non-critical string through an implementation of the mechanism suggested by Strominger of two coincident 5-branes. It is argued that when an instanton shrinks to zero size a tensionless non-critical string appears at the core of the instanton. It is further conjectured that the appearance of tensionless strings in the spectrum leads to new phase transitions in six dimensions in much the same way as massless particles do in four dimensions.

A NOTE ON ZEROES OF SUPERPOTENTIALS IN F-THEORY

We discuss the dependence of superpotential terms in 4D F-theory on moduli parameters. Two cases are studied: the dependence on world-filling 3-brane positions and the dependence on 2-form VEVs. In the first case there is a zero when the 3-brane hits the divisor responsible for the superpotential. In the second case, which has been extensively discussed by Witten in 3D M-theory, there is a zero for special values of 2-form VEVs when the M-theory divisor contains non-trivial 3-cycles. We give an alternative derivation of this fact for the special case of F-theory.

Branes, fluxes and duality in M(atrix) theory

Abstract We use the T - duality transformation which relates M-theory on T 3 to M-theory on a second T 3 with inverse volume to test the Banks-Fischler-Shenker-Susskind suggestion for the matrix model description of M-theory. We find evidence that T - duality is realized as S - duality for U (∞) N = 4 Super-Yang-Mills in (3 + 1) D . We argue that Kaluza-Klein states of gravitons correspond to electric fluxes, wrapped membranes become magnetic fluxes and instantonic membranes are related to Yang-Mills instantons. The T - duality transformation of gravitons into wrapped membranes is interpreted as the duality between electric and magnetic fluxes. The identification of M-theory T - duality as SYM S - duality provides a natural framework for studying the M-theory 5-brane as the S - dual object to the unwrapped membrane. Using the equivalence between compactified M(atrix)-theory and SYM, we find a natural candidate for a description of the light-cone 5-brane of M-theory directly in terms of matrix variables, analogous to the known description of the M(atrix)-theory membrane.

Branes, Calabi-Yau spaces, and toroidal compactification of the N = 1 six-dimensional E8 theory

Abstract We consider compactifications of the N = 1, d = 6, E8 theory on tori to five, four, and three dimensions and learn about some properties of this theory. As a by-product we derive the SL(2, Z ) duality of the N = 2, d = 4, SU(2) theory with Nf = 4. Using this theory on a D-brane probe we shed new light on the singularities of F-theory compactifications to eight dimensions. As another application we consider compactifications of F-theory, M-theory and the IIA string on (singular) Calabi-Yau spaces where our theory appears in space-time. Our viewpoint leads to a new perspective on the nature of the singularities in the moduli space and their space-time interpretations. In particular, we have a universal understanding of how the singularities in the classical moduli space of Calabi-Yau spaces are modified by world-sheet instantons to singularities in the moduli space of the corresponding conformal field theories.

Dipoles, twists and noncommutative gauge theory

T-duality of gauge theories on a noncommutative

Nonlocal field theories and their gravity duals

T^d

Duality and noncommutative gauge theory

can be extended to include fields with twisted boundary conditions. The resulting T-dual theories contain novel nonlocal fields. These fields represent dipoles of constant magnitude. Several unique properties of field theories on noncommutative spaces have simpler counterparts in the dipole-theories.

New perspectives on Yang-Mills theories with sixteen supersymmetries

The gravity duals of nonlocal field theories in the large-N limit exhibit a novel behavior near the boundary. To explore this, we present and study the duals of dipole theories, a particular class of nonlocal theories with fundamental dipole fields. The nonlocal interactions are manifest in the metric of the gravity dual, and type-0 string theories make a surprising appearance. We compare the situation to that in noncommutative super-Yang-Mills theory.

SIX-DIMENSIONAL TENSIONLESS STRINGS IN THE LARGE N LIMIT

We study the generalization of S duality to noncommutative gauge theories. For rank-1 theories, we obtain the leading terms of the dual theory by Legendre transforming the Lagrangian of the noncommutative theory expressed in terms of a commutative gauge field. The dual description is weakly coupled when the original theory is strongly coupled if we appropriately scale the noncommutativity parameter. However, the dual theory appears to be noncommutative in space-time when the original theory is noncommutative in space. This suggests that locality in time for noncommutative theories is an artifact of perturbation theory.

TOROIDAL COMPACTIFICATION OF HETEROTIC 6D NON-CRITICAL STRINGS DOWN TO FOUR DIMENSIONS

We describe various approaches that give matrix descriptions of compactified NS five-branes. As a result, we obtain matrix models for Yang-Mills theories with sixteen supersymmetries in dimensions 2,3,4 and 5. The equivalence of the various approaches relates the Coulomb branch of certain gauge theories to the moduli space of instantons on T4. We also obtain an equivalence between certain six-dimensional string theories. Further, we discuss how various perturbative and non-perturbative features of these Yang-Mills theories appear in their matrix formulations. The matrix model for four-dimensional Yang-Mills is manifestly S-dual. In this case, we describe how electric fluxes, magnetic fluxes and the interaction between vector particles are realized in the matrix model.