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Register a new userA Note on Holographic Non-Relativistic Goldstone Bosons
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We consider a holographic set-up where relativistic invariance is broken by a chemical potential, and a non-abelian internal symmetry is broken spontaneously. We use the tool of holographic renormalization in order to infer what can be learned purely by analytic boundary considerations. We find that the expected Ward identities are correctly reproduced. In particular, we obtain the identity which implies the non-commutation of a pair of broken charges, which leads to the presence of Goldstone bosons with quadratic dispersion relations.
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We consider the interplay between explicit and spontaneous symmetry breaking in strongly coupled field theories. Some well-known statements, such as the Gell-Mann-Oakes-Renner relation, descend directly from the Ward identities and have thus a general relevance. Such Ward identities are recovered in gauge/gravity dual setups through holographic renormalization. In a simple paradigmatic three dimensional toy-model, we find analytic expressions for the two-point correlators which match all the quantum field theoretical expectations. Moreover, we have access to the full spectrum, which is reminiscent of linear confinement.
We develop a holographic model for thermalization following a quench near a quantum critical point with non-trivial dynamical critical exponent. The anti-de Sitter Vaidya null collapse geometry is generalized to asymptotically Lifshitz spacetime. Non-local observables such as two-point functions and entanglement entropy in this background then provide information about the length and time scales relevant to thermalization. The propagation of thermalization exhibits similar horizon behavior as has been seen previously in the conformal case and we give a heuristic argument for why it also appears here. Finally, analytic upper bounds are obtained for the thermalization rates of the non-local observables.
The clockwork mechanism has recently been proposed as a natural way to generate hierarchies among parameters in quantum field theories. The mechanism is characterized by a very specific pattern of spontaneous and explicit symmetry breaking, and the presence of new light states referred to as `gears. In this paper we begin by investigating the self-interactions of these gears in a scalar clockwork model and find a parity-like selection rule at all orders in the fields. We then proceed to investigate how the clockwork mechanism can be realized in 5D linear dilaton models from the spontaneous symmetry breaking of a complex bulk scalar field. We also discuss how the clockwork mechanism is manifest in the scalar components of 5D gauge theories in the linear dilaton model, and build their 4D deconstructed analogue. Finally we discuss attempts at building both 4D and 5D realizations of a non-abelian scalar clockwork mechanism, where in the latter we consider scenarios in which the Goldstone bosons arise from 5D scalar and 5D gauge fields.
Using holographic subregion complexity, we study the confinement-deconfinement phase transition of quantum chromodynamics. In the model we consider here, we observe a connection between the potential energy of probe meson and the behavior of its complexity. Moreover, near the critical point, at which the phase transition takes place, our numerical calculations indicate that we need less information to specify a meson in the non-conformal vacuum than in the conformal one, despite the fact that the non-conformal vacuum has larger energy!
A warped resolved conifold background of type IIB theory, constructed in hep-th/0701064, is dual to the supersymmetric $SU(N)times SU(N)$ gauge theory with a vacuum expectation value (VEV) for one of the bifundamental chiral superfields. This VEV breaks both the superconformal invariance and the baryonic symmetry. The absolute value of the VEV controls the resolution parameter of the conifold. In this paper we study the phase of the VEV, which corresponds to the Goldstone boson of the broken symmetry. We explicitly construct the linearized perturbation of the 4-form R-R potential that contains the Goldstone boson. On general grounds, the theory should contain global strings which create a monodromy of the pseudoscalar Goldstone boson field. We identify these strings with the $D3$-branes wrapping the two-cycle at the tip of the warped resolved conifold.
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