Every isomorphism invariant Borel subset of the space of structures on the natural numbers in a countable relational language is definable in Lω1ω by a theorem of Lopez-Escobar. We derive variants of this result for stabilizer subgroups of the symmetric group Sym(N) for families of relations and non-isomorphism invariant generalized quantifiers on the natural numbers such as “for all even numbe...

We show that all half-BPS Wilson loop operators in N = 4 SYM – which are labeled by Young tableaus – have a gravitational dual description in terms of D5-branes or alternatively in terms of D3-branes in AdS5×S. We prove that the insertion of a half-BPS Wilson loop operator in the N = 4 SYM path integral is achieved by integrating out the degrees of freedom on a configuration of bulk D5-branes o...

A correlator of a Wilson loop with a local operator in N = 4 SYM theory can be represented by a string amplitude in AdS 5 × S 5. This amplitude describes an overlap of the boundary state, which is associated with the loop, with the string mode, which is dual to the local operator. For chiral primary operators with a large R charge, the amplitude can be calculated by semiclassical techniques. We...

Making combined use of the Matrix and Maldacena conjectures, the relation between various thermodynamic transitions in super Yang-Mills (SYM) and supergravity is clarified. The thermodynamic phase diagram of an object in DLCQ M-theory in four and five non-compact space dimensions is constructed; matrix strings, matrix black holes, and black p-branes are among the various phases. Critical manifo...

Following a proposal in ref.[3], we study adding flavors into the MaldacenaNŭnez background. It is achieved by introducing spacetime filling D9-branes or intersecting D5-branes into the background with a wrapping D5-brane. Both D9-branes and D5-branes can be spacetime filling from the 5D bulk point of view. At the probe limit it corresponds to introducing non-chiral fundamental flavors into the...

We discuss various aspect of the holographic correspondence between 5-d gravity and 4-d field theory. First of all, we describe deformations of N = 4 Super Yang-Mills (SYM) theories in terms of 5-d gauged supergravity. In particular, we describe N = 0 and N = 1 deformations of N = 4 SYM to confining theories. Secondly, we describe recent proposals for the holographic dual of the renormalization...

We find regular string duals of three dimensional N = 1 SYM with a Chern-Simons interaction at level k for SO and Sp gauge groups. Using the string dual we exactly reproduce the conjectured pattern of supersymmetry breaking proposed by Witten by showing that there is dynamical supersymmetry breaking for k < h/2 while supersymmetry remains unbroken for k ≥ h/2, where h is the dual Coxeter number...

An exact superpotential is derived for the N = 1 theories which arise as massive deformations of N = 4 supersymmetric Yang-Mills (SYM) theory. The superpotential of the SU(N) theory formulated on R3×S1 is shown to coincide with the complexified potential of the N -body elliptic Calogero-Moser Hamiltonian. This superpotential reproduces the vacuum structure predicted by Donagi and Witten for the...

We compare the two-loop corrections to the finite part of the light-like hexagon Wilson loop with the recent numerical results for the finite part of the MHV six-gluon amplitude in N = 4 SYM theory [hep-th]) and demonstrate that they coincide within the error bars and, at the same time, they differ from the BDS ansatz by a non-trivial function of (dual) conformal kinematical invariants. This pr...

We propose a method for the stabilization of quantum computations (including quantum state storage). The method is based on the operation of projection into SYM, the symmetric subspace of the full state space of R redundant copies of the computer. We describe an efficient algorithm and quantum network effecting SYM–projection and discuss the stabilizing effect of the proposed method in the cont...