Covariant quantization of N=1/2 SYM theories and supergauge invariance

So far, quantum properties of N=1/2 nonanticommutative (NAC) super Yang--Mills theories have been investigated in the WZ gauge. The gauge independence of the results requires assuming that at the quantum level supergauge invariance is not broken by nonanticommutative geometry. In this paper we use an alternative approach which allows studying these theories in a manifestly gauge independent superspace setup. This is accomplished by generalizing the background field method to the NAC case, by moving to a momentum superspace where star products are treated as exponential factors and by developing momentum supergraph techniques. We compute the one--loop gauge effective action for NAC U(N) gauge theories with matter in the adjoint representation. Despite the appearance of divergent contributions which break (super)gauge invariance, we prove that the effective action at this order is indeed invariant.Comment: 24 pages, 3 figures, some references adde

Plane waves from double extended spacetimes

We study exact string backgrounds (WZW models) generated by nonsemisimple algebras which are obtained as double extensions of generic D--dimensional semisimple algebras. We prove that a suitable change of coordinates always exists which reduces these backgrounds to be the product of the nontrivial background associated to the original algebra and two dimensional Minkowski. However, under suitable contraction, the algebra reduces to a Nappi--Witten algebra and the corresponding spacetime geometry, no more factorized, can be interpreted as the Penrose limit of the original background. For both configurations we construct D--brane solutions and prove that {\em all} the branes survive the Penrose limit. Therefore, the limit procedure can be used to extract informations about Nappi--Witten plane wave backgrounds in arbitrary dimensions.Comment: 27 pages, no figures, references adde

Approximation of small-amplitude weakly coupled oscillators with discrete nonlinear Schrodinger equations

Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are approximated by equations of the discrete nonlinear Schrodinger type. We show how to justify this approximation by two methods, which have been very popular in the recent literature. The first method relies on a priori energy estimates and multi-scale decompositions. The second method is based on a resonant normal form theorem. We show that although the two methods are different in the implementation, they produce equivalent results as the end product. We also discuss applications of the discrete nonlinear Schrodinger equation in the context of existence and stability of breathers of the Klein--Gordon lattice

Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein--Gordon lattices

We construct small amplitude breathers in 1D and 2D Klein--Gordon infinite lattices. We also show that the breathers are well approximated by the ground state of the nonlinear Schroedinger equation. The result is obtained by exploiting the relation between the Klein Gordon lattice and the discrete Non Linear Schroedinger lattice. The proof is based on a Lyapunov-Schmidt decomposition and continuum approximation techniques introduced in [7], actually using its main result as an important lemma

On duality and reflection factors for the sinh-Gordon model

The sinh-Gordon model with integrable boundary conditions is considered in low order perturbation theory. It is pointed out that results obtained by Ghoshal for the sine-Gordon breather reflection factors suggest an interesting dual relationship between models with different boundary conditions. Ghoshal's formula for the lightest breather is checked perturbatively to $O(\beta^2)$ in the special set of cases in which the $\phi\to -\phi$ symmetry is maintained. It is noted that the parametrisation of the boundary potential which is natural for the semi-classical approximation also provides a good parametrisation at the `free-fermion' point.Comment: 17 pages, harvmac(b

Exact results in planar N=1 superconformal Yang-Mills theory

In the \beta-deformed N=4 supersymmetric SU(N) Yang-Mills theory we study the class of operators O_J = Tr(\Phi_i^J \Phi_k), i\neq k and compute their exact anomalous dimensions for N,J\to\infty. This leads to a prediction for the masses of the corresponding states in the dual string theory sector. We test the exact formula perturbatively up to two loops. The consistency of the perturbative calculation with the exact result indicates that in the planar limit the one--loop condition g^2=h\bar{h} for superconformal invariance is indeed sufficient to insure the {\em exact} superconformal invariance of the theory. We present a direct proof of this point in perturbation theory. The O_J sector of this theory shares many similarities with the BMN sector of the N=4 theory in the large R--charge limit.Comment: LaTex, 14 pages, 3 figures; v2: minor corrections and one reference adde

Light-like Wilson loops in ABJM and maximal transcendentality

We revisit the computation of the two-loop light-like tetragonal Wilson loop for three dimensional pure Chern-Simons and N=6 Chern-Simons-matter theory, within dimensional regularization with dimensional reduction scheme. Our examination shows that, contrary to prior belief, the result respects maximal transcendentality as is the case of the four-point scattering amplitude of the theory. Remarkably, the corrected result matches exactly the scattering amplitude both in the divergent and in the finite parts, constants included.Comment: 11 page

The 1/2 BPS Wilson loop in ABJ(M) at two loops: The details

We compute the expectation value of the 1/2 BPS circular Wilson loop operator in ABJ(M) theory at two loops in perturbation theory. Our result turns out to be in exact agreement with the weak coupling limit of the prediction coming from localization, including finite N contributions associated to non-planar diagrams. It also confirms the identification of the correct framing factor that connects framing-zero and framing-one expressions, previously proposed. The evaluation of the 1/2 BPS operator is made technically difficult in comparison with other observables of ABJ(M) theory by the appearance of integrals involving the coupling between fermions and gauge fields, which are absent for instance in the 1/6 BPS case. We describe in detail how to analytically solve these integrals in dimensional regularization with dimensional reduction (DRED). By suitably performing the physical limit to three dimensions we clarify the role played by short distance divergences on the final result and the mechanism of their cancellation.Comment: 54 pages, 2 figure

A matrix model for the latitude Wilson loop in ABJM theory

In ABJ(M) theory, we propose a matrix model for the exact evaluation of BPS Wilson loops on a latitude circular contour, so providing a new weak-strong interpolation tool. Intriguingly, the matrix model turns out to be a particular case of that computing torus knot invariants in $U(N_1|N_2)$ Chern-Simons theory. At weak coupling we check our proposal against a three-loop computation, performed for generic framing, winding number and representation. The matrix model is amenable of a Fermi gas formulation, which we use to systematically compute the strong coupling and genus expansions. For the fermionic Wilson loop the leading planar behavior agrees with a previous string theory prediction. For the bosonic operator our result provides a clue for finding the corresponding string dual configuration. Our matrix model is consistent with recent proposals for computing Bremsstrahlung functions exactly in terms of latitude Wilson loops. As a by-product, we extend the conjecture for the exact $B^{\theta}_{1/6}$ Bremsstrahlung function to generic representations and test it with a four-loop perturbative computation. Finally, we propose an exact prediction for $B_{1/2}$ at unequal gauge group ranks.Comment: 73 pages; v2: several improvements, JHEP published versio