Direct Mediation, Duality and Unification

It is well-known that in scenarios with direct gauge mediation of supersymmetry breaking the messenger fields significantly affect the running of Standard Model couplings and introduce Landau poles which are difficult to avoid. This appears to remove any possibility of a meaningful unification prediction and is often viewed as a strong argument against direct mediation. We propose two ways that Seiberg duality can circumvent this problem. In the first, which we call "deflected-unification", the SUSY-breaking hidden sector is a magnetic theory which undergoes a duality to an electric phase, with fewer elementary degrees of freedom coupled to the MSSM. This changes the beta-functions of the MSSM gauge couplings so as to push their Landau poles above the unification scale. We show that this scenario is realised for recently suggested models of gauge mediation based on a metastable SCQD-type hidden sector directly coupled to MSSM. The second possibility, which we call "dual-unification", begins with the observation that, if the mediating fields fall into complete SU(5) multiplets, then the MSSM+messengers exhibits a fake unification at unphysical values of the gauge couplings. We show that, in known examples of electric/magnetic duals, such a fake unification in the magnetic theory reflects a real unification in the electric theory. We therefore propose that the Standard Model could itself be a magnetic dual of some unknown electric theory in which the true unification takes place. This scenario maintains the unification prediction (and unification scale) even in the presence of Landau poles in the magnetic theory below the GUT scale. We further note that this dual realization of grand unification can explain why Nature appears to unify, but the proton does not decay

Three-point functions in N = 4 Yang-Mills theory and pp-waves

Recently it has been proposed that the coefficient of the three-point function of the BMN operators in = 4 supersymmetric Yang-Mills theory is related to the three-string interactions in the pp-wave background. We calculate three-point functions of these operators to the first order in the effective Yang-Mills coupling λ' = gYM2N/J2 in planar perturbation theory. On the string theory side, we derive the explicit expressions of the Neumann matrices to all orders in 1/(μp+α')2. This allows us to compute the corresponding three-string scattering amplitudes. This provides an all orders prediction for the field theory three-point functions. We compare our field theory results with the string theory results to the subleading order in 1/(μp+α')2 and find perfect agreement

Noncommutative QCD, first-order-in-theta-deformed instantons and 't Hooft vertices

For commutative Euclidean time, we study the existence of field configurations that {\it a)} are formal power series expansions in h\theta^{\m\n}, {\it b)} go to ordinary (anti-)instantons as h\theta^{\m\n}\to 0, and {\it c)} render stationary the classical action of Euclidean noncommutative SU(3) Yang-Mills theory. We show that the noncommutative (anti-)self-duality equations have no solutions of this type at any order in h\theta^{\m\n}. However, we obtain all the deformations --called first-order-in-$\theta$-deformed instantons-- of the ordinary instanton that, at first order in h\theta^{\m\n}, satisfy the equations of motion of Euclidean noncommutative SU(3) Yang-Mills theory. We analyze the quantum effects that these field configurations give rise to in noncommutative SU(3) with one, two and three nearly massless flavours and compute the corresponding 't Hooft vertices, also, at first order in h\theta^{\m\n}. Other issues analyzed in this paper are the existence at higher orders in h\theta^{\m\n} of topologically nontrivial solutions of the type mentioned above and the classification of the classical vacua of noncommutative SU(N) Yang-Mills theory that are power series in h\theta^{\m\n}.Comment: Latex. Some macros. No figures. 42 pages. Typos correcte

Noncommutativity from the string perspective: modification of gravity at a mm without mm sized extra dimensions

We explore how the IR pathologies of noncommutative field theory are resolved when the theory is realized as open strings in background B-fields: essentially, since the IR singularities are induced by UV/IR mixing, string theory brings them under control in much the same way as it does the UV singularities. We show that at intermediate scales (where the Seiberg-Witten limit is a good approximation) the theory reproduces the noncommutative field theory with all the (un)usual features such as UV/IR mixing, but that outside this regime, in the deep infra-red, the theory flows continuously to the commutative theory and normal Wilsonian behaviour is restored. The resulting low energy physics resembles normal commutative physics, but with additional suppressed Lorentz violating operators. We also show that the phenomenon of UV/IR mixing occurs for the graviton as well, with the result that, in configurations where Planck's constant receives a significant one-loop correction (for example brane-induced gravity), the distance scale below which gravity becomes non-Newtonian can be much greater than any compact dimensions.Comment: 30 pages. Slight revision: clarified some points and added a referenc

Star product and the general Leigh-Strassler deformation

We extend the definition of the star product introduced by Lunin and Maldacena to study marginal deformations of N=4 SYM. The essential difference from the latter is that instead of considering U(1)xU(1) non-R-symmetry, with charges in a corresponding diagonal matrix, we consider two Z_3-symmetries followed by an SU(3) transformation, with resulting off-diagonal elements. From this procedure we obtain a more general Leigh-Strassler deformation, including cubic terms with the same index, for specific values of the coupling constants. We argue that the conformal property of N=4 SYM is preserved, in both beta- (one-parameter) and gamma_{i}-deformed (three-parameters) theories, since the deformation for each amplitude can be extracted in a prefactor. We also conclude that the obtained amplitudes should follow the iterative structure of MHV amplitudes found by Bern, Dixon and Smirnov.Comment: 21 pages, no figures, JHEP3, v2: references added, v3: appendix A added, v4: clarification in section 3.

Instanton test of non-supersymmetric deformations of the AdS_5 x S^5

We consider instanton effects in a non-supersymmetric gauge theory obtained by marginal deformations of the N=4 SYM. This gauge theory is expected to be dual to type IIB string theory on the AdS_5 times deformed-S^5 background. From an instanton calculation in the deformed gauge theory we extract the prediction for the dilaton-axion field \tau in dual string theory. In the limit of small deformations where the supergravity regime is valid, our instanton result reproduces the expression for \tau of the supergravity solution found by Frolov.Comment: 15 page

Multiinstanton ladders in Baryon Number Violating Processes

We estimate the contribution of a class of multiinstanton ladder graphs to baryon and lepton number violating processes in the standard model. We find that this contribution is negligible and does not alter the high energy behavior of the leading semiclassical approximation.Comment: 15 pages, 2 figures RevTe

Comments on Noncommutative ADHM Construction

We extend the method of matrix partition to obtain explicitly the gauge field for noncommutative ADHM construction in some general cases. As an application of this method we apply it to the U(2) 2-instanton and get explicit result for the gauge fields in the coincident instanton limit. We also easily apply it to the noncommutative 't Hooft instantons in the appendix.Comment: 17 pages, LaTeX; an appendix added, typos corrected, refs adde

Effective actions, Wilson lines and the IR/UV mixing in noncommutative supersymmetric gauge theories

We study IR/UV mixing effects in noncommutative supersymmetric Yang-Mills theories with gauge group U(N) using background field perturbation theory. We compute three- and four-point functions of background fields, and show that the IR/UV mixed contributions to these correlators can be reproduced from an explicitly gauge-invariant effective action, which is expressed in terms of open Wilson lines.Comment: 23 pages, 8 figures. v2: new section and references added, effective action expressed only in terms of open Wilson lines operator

One-Loop Maximal Helicity Violating Amplitudes in N=4 Super Yang-Mills Theories

One-loop maximal helicity violating (MHV) amplitudes in N=4 super Yang-Mills (SYM) theories are analyzed, using the prescription of Cachazo, Svrcek, and Witten (CSW). The relations between leading N_c amplitudes A_{n;1} and sub-leading amplitudes A_{n;c} obtained by the CSW prescription are found to be identical to those obtained from conventional field theory calculations. Combining with existing results, this establishes the validity of the CSW prescription to one-loop in the calculation of MHV amplitudes in N=4 SYM theories of finite N_c.Comment: Minor changes and typos fixed. Published version in JHE