Topological Symmetry Breaking on Einstein Manifolds

It is known that if gauge conditions have Gribov zero modes, then topological symmetry is broken. In this paper we apply it to topological gravity in dimension $n \geq 3$. Our choice of the gauge condition for conformal invariance is $R+{\alpha}=0$ , where $R$ is the Ricci scalar curvature. We find when $\alpha \neq 0$, topological symmetry is not broken, but when $\alpha =0$ and solutions of the Einstein equations exist then topological symmetry is broken. This conditions connect to the Yamabe conjecture. Namely negative constant scalar curvature exist on manifolds of any topology, but existence of nonnegative constant scalar curvature is restricted by topology. This fact is easily seen in this theory. Topological symmetry breaking means that BRS symmetry breaking in cohomological field theory. But it is found that another BRS symmetry can be defined and physical states are redefined. The divergence due to the Gribov zero modes is regularized, and the theory after topological symmetry breaking become semiclassical Einstein gravitational theory under a special definition of observables.Comment: 16 pages, Late

Yangian Symmetry for Bi-Scalar Loop Amplitudes

We establish an all-loop conformal Yangian symmetry for the full set of planar amplitudes in the recently proposed integrable bi-scalar field theory in four dimensions. This chiral theory is a particular double scaling limit of gamma-twisted weakly coupled N=4 SYM theory. Each amplitude with a certain order of scalar particles is given by a single fishnet Feynman graph of disc topology cut out of a regular square lattice. The Yangian can be realized by the action of a product of Lax operators with a specific sequence of inhomogeneity parameters on the boundary of the disc. Based on this observation, the Yangian generators of level one for generic bi-scalar amplitudes are explicitly constructed. Finally, we comment on the relation to the dual conformal symmetry of these scattering amplitudes.Comment: 40 pages, 20 figure

Exact solutions with AdS asymptotics of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field

We propose a general method for solving exactly the static field equations of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field. Our method starts from an ansatz for the scalar field profile, and determines, together with the metric functions, the corresponding form of the scalar self-interaction potential. Using this method we prove a new no-hair theorem about the existence of hairy black-hole and black-brane solutions and derive broad classes of static solutions with radial symmetry of the theory, which may play an important role in applications of the AdS/CFT correspondence to condensed matter and strongly coupled QFTs. These solutions include: 1) four- or generic $(d+2)$-dimensional solutions with planar, spherical or hyperbolic horizon topology; 2) solutions with AdS, domain wall and Lifshitz asymptotics; 3) solutions interpolating between an AdS spacetime in the asymptotic region and a domain wall or conformal Lifshitz spacetime in the near-horizon region.Comment: Some references adde

Super-Group Field Cosmology

In this paper we construct a model for group field cosmology. The classical equations of motion for the non-interactive part of this model generate the Hamiltonian constraint of loop quantum gravity for a homogeneous isotropic universe filled with a scalar matter field. The interactions represent topology changing processes that occurs due to joining and splitting of universes. These universes in the multiverse are assumed to obey both bosonic and fermionic statistics, and so a supersymmetric multiverse is constructed using superspace formalism. We also introduce gauge symmetry in this model. The supersymmetry and gauge symmetry are introduced at the level of third quantized fields, and not the second quantized ones. This is the first time that supersymmetry has been discussed at the level of third quantized fields.Comment: 14 pages, 0 figures, accepted for publication in Class. Quant. Gra

Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere

We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to different commutative or non-commutative spaces. We present some of the theories which have been investigated in this framework, with a particular attention to the scalar model. Then we comment on the results recently obtained from Monte Carlo simulations, and show a preview of new numerical data, which are consistent with the expected transition between two phases characterised by the topology of the support of a matrix eigenvalue distribution.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Toward the minimal realization of a light composite Higgs

Work in progress is reported on a particularly interesting gauge theory with a fermion doublet in the two-index symmetric (sextet) representation of the SU(3) color gauge group. Extending previous studies we outline our strategy as we investigate Goldstone dynamics and Electroweak scale setting from chiral symmetry breaking ($\chi$ SB), test the GMOR relation from the spectrum of the Dirac operator and the related chiral condensate, begin to develop and test mixed action based improved analysis of $\chi$ SB with new run plans at fixed topology to cross over from the p-regime to the epsilon-regime of $\chi$ SB, continue to pursue the light $0^{++}$ scalar and its relation to the dilaton, and probe the scale-dependent running coupling from the perturbative UV scale to the scale of chiral symmetry breaking. Our observations suggest that the model is very close to the conformal window and a light composite scalar, perhaps the Higgs impostor with or without dilaton-like interpretation, appears to emerge with $0^{++}$ quantum numbers. The lightest baryon of the model on the 3 TeV scale has intriguing implications.Comment: 14 pages, 7 figures, The 32nd International Symposium on Lattice Field Theory,23-28 June, 2014 Columbia University, New York, NY, US

Localizing gravity on thick branes: a solution for massive KK modes of the Schroedinger equation

We generate scalar thick brane configurations in a 5D Riemannian space time which describes gravity coupled to a self-interacting scalar field. We also show that 4D gravity can be localized on a thick brane which does not necessarily respect Z_2-symmetry, generalizing several previous models based on the Randall-Sundrum system and avoiding the restriction to orbifold geometries as well as the introduction of the branes in the action by hand. We begin by obtaining a smooth brane configuration that preserves 4D Poincar'e invariance and violates reflection symmetry along the fifth dimension. The extra dimension can have either compact or extended topology, depending on the values of the parameters of the solution. In the non-compact case, our field configuration represents a thick brane with positive energy density centered at y=c_2, whereas in the compact case we get pairs of thick branes. We recast as well the wave equations of the transverse traceless modes of the linear fluctuations of the classical solution into a Schroedinger's equation form with a volcano potential of finite bottom. We solve Schroedinger equation for the massless zero mode m^2=0 and obtain a single bound wave function which represents a stable 4D graviton and is free of tachyonic modes with m^2<0. We also get a continuum spectrum of Kaluza-Klein (KK) states with m^2>0 that are suppressed at y=c_2 and turn asymptotically into plane waves. We found a particular case in which the Schroedinger equation can be solved for all m^2>0, giving us the opportunity of studying analytically the massive modes of the spectrum of KK excitations, a rare fact when considering thick brane configurations.Comment: 8 pages in latex. We corrected signs in the field equations, the expressions for the scalar field and the self-interacting potential. Due to the fact that no changes are introduced in the warp factor, the physics of the system remains the sam

Decoupling of Heavy Kaluza-Klein Modes In Models With Five-Dimensional Scalar Fields

We investigate the decoupling of heavy Kaluza-Klein modes in $\phi^{4}$ theory and scalar QED with space-time topology $\mathbb{R}^{3,1} \times S^{1}$. We calculate the effective action due to integrating out heavy KK modes. We construct generalized RGE's for the couplings with respect to the compactification scale $M$. With the solutions to the RGE's we find the $M$-scale dependence of the effective theory due to higher dimensional quantum effects. We find that the heavy modes decouple in $\phi^{4}$ theory, but do not decouple in scalar QED. This is due to the zero mode of the 5-th component $A_{5}$ of the 5-d gauge field. Because $A_{5}$ is a scalar under 4-d Lorentz transformations, there is no gauge symmetry protecting it from getting mass and $A_{5}^{4}$ interaction terms after loop corrections. In light of these unpleasant features, we explore $S^{1}/\mathbb{Z}_{2}$ compactifications, which eliminate $A_{5}$, allowing for the heavy modes to decouple at low energies. We also explore the possibility of decoupling by including higher dimensional operators. It is found that this is possible, but a high degree of fine tuning is required.Comment: 9 pages, no figures; sign error on equations 20, 36, 37; Added additional reference