Gluon Scattering Amplitudes in Finite Temperature Gauge/Gravity Dualities

We examine the gluon scattering amplitude in N=4 super Yang-Mills at finite temperature with nonzero R-charge densities, and in Non-Commutative gauge theory at finite temperature. The gluon scattering amplitude is defined as a light-like Wilson loop which lives at the horizon of the T-dual black holes of the backgrounds we consider. We study in detail a special amplitude, which corresponds to forward scattering of a low energy gluon off a high energy one. For this kinematic configuration in the considered backgrounds, we find the corresponding minimal surface which is directly related to the gluon scattering amplitude. We find that for increasing the chemical potential or the non-commutative parameter, the on-shell action corresponding to our Wilson loop in the T-dual space decreases. For all of our solutions the length of the short side of the Wilson loop is constrained by an upper bound which depends on the temperature, the R-charge density and the non-commutative parameter. Due to this constraint, in the limit of zeroth temperature our approach breaks down since the upper bound goes to zero, while by keeping the temperature finite and letting the chemical potential or the non-commutative parameter to approach to zero the limit is smooth.Comment: 30 pages, 16 figures, minor corrections (plus improved numerical computation for the non-commutative case

Constraining noncommutative field theories with holography

An important window to quantum gravity phenomena in low energy noncommutative (NC) quantum field theories (QFTs) gets represented by a specific form of UV/IR mixing. Yet another important window to quantum gravity, a holography, manifests itself in effective QFTs as a distinct UV/IR connection. In matching these two principles, a useful relationship connecting the UV cutoff $\Lambda_{\rm UV}$, the IR cutoff $\Lambda_{\rm IR}$ and the scale of noncommutativity $\Lambda_{\rm NC}$, can be obtained. We show that an effective QFT endowed with both principles may not be capable to fit disparate experimental bounds simultaneously, like the muon $g-2$ and the masslessness of the photon. Also, the constraints from the muon $g-2$ preclude any possibility to observe the birefringence of the vacuum coming from objects at cosmological distances. On the other hand, in NC theories without the UV completion, where the perturbative aspect of the theory (obtained by truncating a power series in $\Lambda_{\rm NC}^{-2}$) becomes important, a heuristic estimate of the region where the perturbative expansion is well-defined $E/ \Lambda_{\rm NC} \lesssim 1$, gets affected when holography is applied by providing the energy of the system $E$ a $\Lambda_{\rm NC}$-dependent lower limit. This may affect models which try to infer the scale $\Lambda_{\rm NC}$ by using data from low-energy experiments.Comment: 4 pages, version to be published in JHE

A manifestly MHV Lagrangian for N=4 Yang-Mills

We derive a manifestly MHV Lagrangian for the N=4 supersymmetric Yang-Mills theory in light-cone superspace. This is achieved by constructing a canonical redefinition which maps the N=4 superfield and its conjugate to a new pair of superfields. In terms of these new superfields the N=4 Lagrangian takes a (non-polynomial) manifestly MHV form, containing vertices involving two superfields of negative helicity and an arbitrary number of superfields of positive helicity. We also discuss constraints satisfied by the new superfields, which ensure that they describe the correct degrees of freedom in the N=4 supermultiplet. We test our derivation by showing that an expansion of our superspace Lagrangian in component fields reproduces the correct gluon MHV vertices.Comment: 37 pages, 1 figure. v2: minor changes, references adde

Quantum Symmetries and Marginal Deformations

We study the symmetries of the N=1 exactly marginal deformations of N=4 Super Yang-Mills theory. For generic values of the parameters, these deformations are known to break the SU(3) part of the R-symmetry group down to a discrete subgroup. However, a closer look from the perspective of quantum groups reveals that the Lagrangian is in fact invariant under a certain Hopf algebra which is a non-standard quantum deformation of the algebra of functions on SU(3). Our discussion is motivated by the desire to better understand why these theories have significant differences from N=4 SYM regarding the planar integrability (or rather lack thereof) of the spin chains encoding their spectrum. However, our construction works at the level of the classical Lagrangian, without relying on the language of spin chains. Our approach might eventually provide a better understanding of the finiteness properties of these theories as well as help in the construction of their AdS/CFT duals.Comment: 1+40 pages. v2: minor clarifications and references added. v3: Added an appendix, fixed minor typo