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Register a new userThe gravity dual to a quantum critical point with spontaneous symmetry breaking
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We consider zero temperature solutions to the Abelian Higgs model coupled to gravity with a negative cosmological constant. With appropriate choices of parameters, the geometry contains two copies of anti-de Sitter space, one describing conformal invariance in the ultraviolet, and one in the infrared. The effective speed of signal propagation is smaller in the infrared. Greens functions and associated transport coefficients can have unusual power law scaling in the infrared. We provide an example in which the real part of the conductivity scales approximately as omega^3.5 for small omega.
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We study a lattice model of interacting Dirac fermions in $(2+1)$ dimension space-time with an SU(4) symmetry. While increasing interaction strength, this model undergoes a {it continuous} quantum phase transition from the weakly interacting Dirac semimetal to a fully gapped and nondegenerate phase without condensing any Dirac fermion bilinear mass operator. This unusual mechanism for mass generation is consistent with recent studies of interacting topological insulators/superconductors, and also consistent with recent progresses in lattice QCD community.
Weyl invariant theories of scalars and gravity can generate all mass scales spontaneously, initiated by a dynamical process of inertial spontaneous symmetry breaking that does not involve a potential. This is dictated by the structure of the Weyl current, $K_mu$, and a cosmological phase during which the universe expands and the Einstein-Hilbert effective action is formed. Maintaining exact Weyl invariance in the renormalised quantum theory is straightforward when renormalisation conditions are referred back to the VEVs of fields in the action of the theory, which implies a conserved Weyl current. We do not require scale invariant regulators. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential.
We study quadratic gravity $R^2+R_{[mu u]}^2$ in the Palatini formalism where the connection and the metric are independent. This action has a {it gauged} scale symmetry (also known as Weyl gauge symmetry) of Weyl gauge field $v_mu= (tildeGamma_mu-Gamma_mu)/2$, with $tildeGamma_mu$ ($Gamma_mu$) the trace of the Palatini (Levi-Civita) connection, respectively. The underlying geometry is non-metric due to the $R_{[mu u]}^2$ term acting as a gauge kinetic term for $v_mu$. We show that this theory has an elegant spontaneous breaking of gauged scale symmetry and mass generation in the absence of matter, where the necessary scalar field ($phi$) is not added ad-hoc to this purpose but is extracted from the $R^2$ term. The gauge field becomes massive by absorbing the derivative term $partial_mulnphi$ of the Stueckelberg field (dilaton). In the broken phase one finds the Einstein-Proca action of $v_mu$ of mass proportional to the Planck scale $Msim langlephirangle$, and a positive cosmological constant. Below this scale $v_mu$ decouples, the connection becomes Levi-Civita and metricity and Einstein gravity are recovered. These results remain valid in the presence of non-minimally coupled scalar field (Higgs-like) with Palatini connection and the potential is computed. In this case the theory gives successful inflation and a specific prediction for the tensor-to-scalar ratio $0.007leq r leq 0.01$ for current spectral index $n_s$ (at $95%$CL) and N=60 efolds. This value of $r$ is mildly larger than in inflation in Weyl quadratic gravity of similar symmetry, due to different non-metricity. This establishes a connection between non-metricity and inflation predictions and enables us to test such theories by future CMB experiments.
We study a theory where the presence of an extra spin-two field coupled to gravity gives rise to a phase with spontaneously broken Lorentz symmetry. In this phase gravity is massive, and the Weak Equivalence Principle is respected. The newtonian potentials are in general modified, but we identify an non-perturbative symmetry that protects them. The gravitational waves sector has a rich phenomenology: sources emit a combination of massless and massive gravitons that propagate with distinct velocities and also oscillate. Since their velocities differ from the speed of light, the time of flight difference between gravitons and photons from a common source could be measured.
We study phase structure of mass-deformed ABJM theory which is a three dimensional $mathcal{N}=6$ superconformal theory deformed by mass parameters and has the gauge group $text{U}(N)times text{U}(N)$ with Chern-Simons levels $(k,-k)$ which may have a gravity dual. We discuss that the mass deformed ABJM theory on $S^3$ breaks supersymmetry in a large-$N$ limit if the mass is larger than a critical value. To see some evidence for this conjecture, we compute the partition function exactly, and numerically by using the Monte Carlo Simulation for small $N$. We discover that the partition function has zeroes as a function of the mass deformation parameters if $Nge k$, which supports the large-$N$ supersymmetry breaking. We also find a solution to the large-$N$ saddle point equations, where the free energy is consistent with the finite $N$ result.
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