Dynamics of Fundamental Matter in N=2* Yang-Mills Theory

We study the dynamics of quenched fundamental matter in $\mathcal{N}=2^\ast$ supersymmetric large $N$ SU(N) Yang-Mills theory at zero temperature. Our tools for this study are probe D7-branes in the holographically dual $\mathcal{N}=2^\ast$ Pilch-Warner gravitational background. Previous work using D3-brane probes of this geometry has shown that it captures the physics of a special slice of the Coulomb branch moduli space of the gauge theory, where the $N$ constituent D3-branes form a dense one dimensional locus known as the enhancon, located deep in the infrared. Our present work shows how this physics is supplemented by the physics of dynamical flavours, revealed by the D7-branes embeddings we find. The Pilch-Warner background introduces new divergences into the D7-branes free energy, which we are able to remove with a single counterterm. We find a family of D7-brane embeddings in the geometry and discuss their properties. We study the physics of the quark condensate, constituent quark mass, and part of the meson spectrum. Notably, there is a special zero mass embedding that ends on the enhancon, which shows that while the geometry acts repulsively on the D7-branes, it does not do so in a way that produces spontaneous chiral symmetry breaking.Comment: 24 pages, 8 figures. Corrected typos, added comment about counterterm. To appear in JHE

On the rotating wave approximation in the adiabatic limit

I revisit a longstanding question in quantum optics; When is the rotating wave approximation justified? In terms of the Jaynes-Cummings and Rabi models I demonstrate that the approximation in general breaks down in the adiabatic limit regardless of system parameters. This is explicitly shown by comparing Berry phases of the two models, where it is found that this geometrical phase is strictly zero in the Rabi model contrary to the non-trivial Berry phase of the Jaynes-Cummings model. The source of this surprising result is traced back to different topologies in the two models.Comment: 8 pages, 3 figure

Chiral Symmetry Breaking and External Fields in the Kuperstein-Sonnenschein Model

A novel holographic model of chiral symmetry breaking has been proposed by Kuperstein and Sonnenschein by embedding non-supersymmetric probe D7 and anti-D7 branes in the Klebanov-Witten background. We study the dynamics of the probe flavours in this model in the presence of finite temperature and a constant electromagnetic field. In keeping with the weakly coupled field theory intuition, we find the magnetic field promotes spontaneous breaking of chiral symmetry whereas the electric field restores it. The former effect is universally known as the "magnetic catalysis" in chiral symmetry breaking. In the presence of an electric field such a condensation is inhibited and a current flows. Thus we are faced with a steady-state situation rather than a system in equilibrium. We conjecture a definition of thermodynamic free energy for this steady-state phase and using this proposal we study the detailed phase structure when both electric and magnetic fields are present in two representative configurations: mutually perpendicular and parallel.Comment: 50 pages, multiple figures, minor typo fixed, references adde

Stationary strings and branes in the higher-dimensional Kerr-NUT-(A)dS spacetimes

We demonstrate complete integrability of the Nambu-Goto equations for a stationary string in the general Kerr-NUT-(A)dS spacetime describing the higher-dimensional rotating black hole. The stationary string in D dimensions is generated by a 1-parameter family of Killing trajectories and the problem of finding a string configuration reduces to a problem of finding a geodesic line in an effective (D-1)-dimensional space. Resulting integrability of this geodesic problem is connected with the existence of hidden symmetries which are inherited from the black hole background. In a spacetime with p mutually commuting Killing vectors it is possible to introduce a concept of a $\xi$-brane, that is a p-brane with the worldvolume generated by these fields and a 1-dimensional curve. We discuss integrability of such $\xi$-branes in the Kerr-NUT-(A)dS spacetime.Comment: 8 pages, no figure

Thermal Dynamics of Quarks and Mesons in N=2* Yang-Mills Theory

We study the dynamics of quenched fundamental matter in $\mathcal{N}=2^\ast$ supersymmetric large $N_c$ $SU(N_c)$ Yang-Mills theory, extending our earlier work to finite temperature. We use probe D7-branes in the holographically dual thermalized generalization of the $\mathcal{N}=2^\ast$ Pilch-Warner gravitational background found by Buchel and Liu. Such a system provides an opportunity to study how key features of the dynamics are affected by being in a non-conformal setting where there is an intrinsic scale, set here by the mass, $m_H$, of a hypermultiplet. Such studies are motivated by connections to experimental studies of the quark-gluon plasma at RHIC and LHC, where the microscopic theory of the constituents, QCD, has a scale, $\Lambda_{\rm QCD}$. We show that the binding energy of mesons in the $\mathcal{N}=2^\ast$ theory is increased in the presence of the scale $m_H$, and that subsequently the meson-melting temperature is higher than for the conformal case.Comment: 17 pages, 6 figure

Holographic phase transitions at finite baryon density

We use holographic techniques to study SU(Nc) super Yang-Mills theory coupled to Nf << Nc flavours of fundamental matter at finite temperature and baryon density. We focus on four dimensions, for which the dual description consists of Nf D7-branes in the background of Nc black D3-branes, but our results apply in other dimensions as well. A non-zero chemical potential mu or baryon number density n is introduced via a nonvanishing worldvolume gauge field on the D7-branes. Ref. [1] identified a first order phase transition at zero density associated with `melting' of the mesons. This extends to a line of phase transitions for small n, which terminates at a critical point at finite n. Investigation of the D7-branes' thermodynamics reveals that (d mu / dn)_T <0 in a small region of the phase diagram, indicating an instability. We comment on a possible new phase which may appear in this region.Comment: 33 pages, 22 figure

Quantum Adiabatic Markovian Master Equations

We develop from first principles Markovian master equations suited for studying the time evolution of a system evolving adiabatically while coupled weakly to a thermal bath. We derive two sets of equations in the adiabatic limit, one using the rotating wave (secular) approximation that results in a master equation in Lindblad form, the other without the rotating wave approximation but not in Lindblad form. The two equations make markedly different predictions depending on whether or not the Lamb shift is included. Our analysis keeps track of the various time- and energy-scales associated with the various approximations we make, and thus allows for a systematic inclusion of higher order corrections, in particular beyond the adiabatic limit. We use our formalism to study the evolution of an Ising spin chain in a transverse field and coupled to a thermal bosonic bath, for which we identify four distinct evolution phases. While we do not expect this to be a generic feature, in one of these phases dissipation acts to increase the fidelity of the system state relative to the adiabatic ground state.Comment: 31 pages, 9 figures. v2: Generalized Markov approximation bound. Included a section on thermal equilibration. v3: Added text that appears in NJP version. Generalized Lindblad ME to include degenerate subspaces. v3. Corrections made to Appendix E and F. We thank Kabuki Takada and Hidetoshi Nishimori for pointing out the errors. v4: Corrected a typo in Eqt. B

Moving Defects in AdS/CFT

We study defects of various dimensions moving through Anti-de Sitter space. Using the AdS/CFT correspondence this allows us to probe aspects of the dual quantum field theory. We focus on the energy loss experienced by these defects as they move through the CFT plasma. We find that the behavior of these physical quantities is governed by induced world-volume horizons. We identify world-volume analogs for several gravitational phenomena including black holes, the Hawking-Page phase transition and expanding cosmological horizons.Comment: 24 pages, 7 figures. Version 2 contains two added reference

Holographic Superconductors in a Cohesive Phase

We consider a four-dimensional N=2 gauged supergravity coupled to matter fields. The model is obtained by a U(1) gauging of a charged hypermultiplet and therefore it is suitable for the study of holographic superconductivity. The potential has a topologically flat direction and the parameter running on this "moduli space" labels the new superconducting black holes. Zero temperature solutions are constructed and the phase diagram of the theory is studied. The model has rich dynamics. The retrograde condensate is just a special case in the new class of black holes. The calculation of the entanglement entropy makes manifest the properties of a generic solution and the superconductor at zero temperature is in a confined cohesive phase. The parameter running on the topologically flat direction is a marginal coupling in the dual field theory. We prove this statement by considering the way double trace deformations are treated in the AdS/CFT correspondence. Finally, we comment on a possible connection, in the context of gauge/gravity dualities, between the geometry of the scalar manifold in N=2 supergravity models and the space of marginal deformations of the dual field theory.Comment: 32 pages, 11 figures. Introduction rewritten and clarified, comments and details on section 4 added, acknowledgements rectified. To appear in JHE

Magnetic Catalysis in AdS4

We study the formation of fermion condensates in Anti de Sitter space. In particular, we describe a novel version of magnetic catalysis that arises for fermions in asymptotically AdS4 geometries which cap off in the infra-red with a hard wall. We show that the presence of a magnetic field induces a fermion condensate in the bulk that spontaneously breaks CP symmetry. From the perspective of the dual boundary theory, this corresponds to a strongly coupled version of magnetic catalysis in d=2+1.Comment: 22 pages, 4 figures. v2: References added, factors of 2 corrected, extra comments added in appendix. v3: extra comments about fermion modes in a hard wall background. v4: A final factor of