Transições de Fase nas Teorias Holográficas sem Supersimetria - Silva, Ulysses Camara da (2013)
According to the gauge/gravity correspondence rules, the holographic description of certainstrongly coupledQF Td-1at infinite volume and zero temperature is based on the particularflat Domain Walls (DW’s) solutions of their duald-dimensional Gravity models. The mainproblem addressed in the present thesis concerns the systematic application of the Gauss-Bonnet (GB) and cubic Quasi-Topological Gravity (QTG) DW’s to the investigation of theRenormalization Group (RG) properties and of the phase structure of theirQF Td-1’s duals.It represents an off-critical extension of the recent holographic studies of a family ofa!=cCF Td-1’s with non-vanishing energy flux parametert4.We derive a BPS-like first order system of equations for a family of flat static DW’s for the GBand cubic QTG extensions of Einstein Gravity coupled to massive scalar self-interacting matter,by introducing an appropriate matter superpotential. The knowledge of such DW’s solutions,allows us to construct the exactQF T’s beta-functions, as well as of the trace anomaliesa(l)andc(l), in terms of the corresponding superpotentials. As a consequence, we are ableto determine the complete set ofCF T'sdata characterizing the universality classes of theUV and IR critical points and to follow the particular RG evolution of this data. We furtheranalyse the dependence of the critical properties of such dualQF T’s on the values of thegravitational GB’s and QT couplings and on the shape of the considered superpotentials. Forodd values ofd, the explicit form of the “a- andc-central charges”, as functions of the runningcoupling constant, enable us to establish the conditions under which thea&c-Theorems fortheir decreasing are valid. The restrictions imposed on the massless Holographic RG flows bythe requirements of the positivity of the energy fluxes are also derived. Few specific polinomialsuperpotentials are studied in detail.They provide examples of unitary dualQF T’s having c!=acritical points representing second or infinite order phase transitions. Depending onthe range of the values of the coupling constant, they exhibit massive and massless phases,described by a chain of distinct DW’s solutions sharing common boundaries.We have also found an extension of the superpotential method for GB’s and cubic Quasi-Topological Gravity coupled to an arbitrary number of interacting scalar fields. For appropriatechoices of the matter superpotentials, theirphase diagrams turn out to have the well knownBerezinski-Kosterletz-Thouless form, with aline of second order phase transitions at weakcoupling and specific infinite order massless-to-massive phase transitions in the cross-overregion.The aim of the present research is to provide more arguments in favour of the conjecturethat by holographic calculations based ond=5GB and cubic QT Gravity models one canreproduce the strong coupling limits of certain unitary (non-supersymmetric)QF T4’s, whosemassive and massless phases exhibit “phenomenologically reasonable” off-critical features.