Holographic entanglement chemistry
(Submitted on 2 May 2016)
We use the Iyer-Wald formalism to derive an extended first law of entanglement that includes variations in the cosmological constant, Newton’s constant and –in the case of higher derivative theories– all the additional couplings of the theory. In Einstein gravity, where the number of degrees of freedom N2 of the dual field theory is a function of Λ and G, our approach allows us to vary N keeping the field theory scale fixed or to vary the field theory scale keeping N fixed. We also derive an extended first law of entanglement for Gauss-Bonnet and Lovelock gravity.
Contact Hamiltonian Mechanics
(Submitted on 27 Apr 2016)
In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.
Polarized 3 parton production in inclusive DIS at small x
(Submitted on 28 Apr 2016)
Azimuthal angular correlations between produced hadrons/jets in high energy collisions are a sensitive probe of the dynamics of QCD at small x. Here we derive the triple differential cross section for inclusive production of 3 polarized partons in DIS at small x using the spinor helicity formalism. The target proton or nucleus is described using the Color Glass Condensate (CGC) formalism. The resulting expressions are used to study azimuthal angular correlations between produced partons in order to probe the gluon structure of the target hadron or nucleus. Our analytic expressions can also be used to calculate the real part of the Next to Leading Order (NLO) corrections to di-hadron production in DIS by integrating out one of the three final state partons.
Non-Archimedean Reaction-Ultradiffusion Equations and Complex Hierarchic Systems
(Submitted on 21 Apr 2016)
We initiate the study of non-Archimedean reaction-ultradiffusion equations and their connections with models of complex hierarchic systems. From a mathematical perspective, the equations studied here are the p-adic counterpart of the integro-differential models for phase separation introduced by Bates and Chmaj. Our equations are also generalizations of the ultradiffusion equations on trees studied in the 80’s by Ogielski, Stein, Bachas, Huberman, among others, and also generalizations of the master equations of the Avetisov et al. models, which describe certain complex hierarchic systems. From a physical perspective, our equations are gradient flows of non-Archimedean free energy functionals and their solutions describe the macroscopic density profile of a bistable material whose space of states has an ultrametric structure. Some of our results are p-adic analogs of some well-known results in the Archimedean settting, however, the mechanism of diffusion is completely different due to the fact that it occurs in an ultrametric space.
Second order differential realization of the Bargmann-Wigner framework for particles of any spin
(Submitted on 22 Apr 2016)
The Bargmann-Wigner (BW) framework describes particles of spin-j in terms of Dirac spinors of rank 2j, obtained as the local direct product of n Dirac spinor copies, with n=2j. Such spinors are reducible, and contain also (j,0)+(0,j)-pure spin representation spaces. The 2(2j+1) degrees of freedom of the latter are identified by a projector given by the n-fold direct product of the covariant parity projector within the Dirac spinor space. Considering totally symmetric tensor spinors one is left with the expected number of 2(2j+1) independent degrees of freedom. The BW projector is of the order ∂2j in the derivatives, and so are the related spin-j wave equations and associated Lagrangians. High order differential equations can not be consistently gauged, and allow several unphysical aspects, such as non-locality, acausality, ghosts and etc to enter the theory. In order to avoid these difficulties we here suggest a strategy of replacing the high order of the BW wave equations by the universal second order. To do so we replaced the BW projector by one of zeroth order in the derivatives. We built it up from one of the Casimir invariants of the Lorentz group when exclusively acting on spaces of internal spin degrees of freedom. This projector allows one to identify anyone of the irreducible sectors of the primordial rank-2j spinor, in particular (j,0)+(0,j), and without any reference to the external space-time and the four-momentum. The dynamics is then introduced by requiring the (j,0)+ (0,j) sector to satisfy the Klein-Gordon equation. The scheme allows for a consistent minimal gauging.
Four-dimensional unsubtraction from the loop-tree duality
(Submitted on 22 Apr 2016)
We present a new algorithm to construct a purely four dimensional representation of higher-order perturbative corrections to physical cross-sections at next-to-leading order (NLO). The algorithm is based on the loop-tree duality (LTD), and it is implemented by introducing a suitable mapping between the external and loop momenta of the virtual scattering amplitudes with the external momenta of the real emission corrections. In this way, the sum over degenerate infrared states is performed at the integrand level and the cancellation of infrared divergences occurs locally without introducing subtraction counter-terms to deal with soft and final-state collinear singularities. The dual representation of ultraviolet counter-terms is also discussed in detail, in particular for self-energy contributions. The method is first illustrated with the scalar three-point function, before proceeding with the calculation of the physical cross-section for γ∗→qq¯(g), at its generalisation to multi-leg processes. The extension to next-to-next-to-leading order (NNLO) is briefly commented.
Finite temperature QCD: Quarkonium survival at and beyond Tc and dimuon production in heavy ion collisions
(Submitted on 22 Apr 2016)
Finite temperature QCD sum rules are applied to the behaviour of charmonium and bottonium states, leading to their survival at and beyond the critical temperature for deconfinement. Di-muon production in heavy-ion collisions in the ρ-region is also discussed.