Large N (=3) Neutrinos and Random Matrix Theory

The large N limit has been successfully applied to QCD, leading to qualitatively correct results even for N=3. In this work, we propose to treat the number N=3 of Standard Model generations as a large number. Specifically, we apply this idea to the neutrino anarchy scenario and study neutrino physics using Random Matrix Theory, finding new results in both areas. For neutrino physics, we obtain predictions for the masses and mixing angles as a function of the generation number N. The Seesaw mechanism produces a hierarchy of order 1/N^3 between the lightest and heaviest neutrino, and a theta(13) mixing angle of order 1/N, in parametric agreement with experimental data when N goes to 3. For Random Matrix Theory, this motivates the introduction of a new type of ensemble of random matrices, the "Seesaw ensemble." Basic properties of such matrices are studied, including the eigenvalue density and the interpretation as a Coulomb gas system. Besides its mathematical interest, the Seesaw ensemble may be useful in random systems where two hierarchical scales exist.Comment: 20 pages, 6 figures, 1 table; accepted version for JHEP, references adde

Quantum critical metals in 4−ϵ4-\epsilon dimensions

We study the quantum theory of a Fermi surface coupled to a gapless boson scalar in $D=4-\epsilon$ spacetime dimensions as a simple model for non-Fermi liquids (NFL) near a quantum phase transition. Our analysis takes into account the full backreaction from Landau damping of the boson, and obtains an RG flow that proceeds through three distinct stages. Above the scale of Landau damping the Fermi velocity flows to zero, while the coupling evolves according to its classical dimension. Once damping becomes important, its backreaction leads to a crossover regime where dynamic and static damping effects compete and the fermion self-energy does not respect scaling. Below this crossover and having tuned the boson to criticality, the theory flows to a $z=3$ scalar interacting with a NFL. By increasing the number of bosonic flavors, the phase diagram near the quantum critical point interpolates between a superconducting dome fully covering the NFL behavior, and a phase where NFL effects become important first, before the onset of superconductivity. A generic prediction of the theory is that the Fermi velocity and quasiparticle residue vanish with a power-law $\omega^\epsilon$ as the fixed point is approached. These features may be useful for understanding some of the phenomenology of high $T_c$ materials in a systematic $\epsilon$--expansion.Comment: 38 pages, 6 figures. v2: comments and references added; version published in PR

Black branes in flux compactifications

We construct charged black branes in type IIA flux compactifications that are dual to (2+1)-dimensional field theories at finite density. The internal space is a general Calabi-Yau manifold with fluxes, with internal dimensions much smaller than the AdS radius. Gauge fields descend from the 3-form RR potential evaluated on harmonic forms of the Calabi-Yau, and Kaluza-Klein modes decouple. Black branes are described by a four-dimensional effective field theory that includes only a few light fields and is valid over a parametrically large range of scales. This effective theory determines the low energy dynamics, stability and thermodynamic properties. Tools from flux compactifications are also used to construct holographic CFTs with no relevant scalar operators, that can lead to symmetric phases of condensed matter systems stable to very low temperatures. The general formalism is illustrated with simple examples such as toroidal compactifications and manifolds with a single size modulus. We initiate the classification of holographic phases of matter described by flux compactifications, which include generalized Reissner-Nordstrom branes, nonsupersymmetric $AdS_2 \times R^2$ and hyperscaling violating solutions.Comment: 37 pages, 2 figures, typos corrected and comments adde

Supersymmetric Defect Models and Mirror Symmetry

We study supersymmetric field theories in three space-time dimensions doped by various configurations of electric charges or magnetic fluxes. These are supersymmetric avatars of impurity models. In the presence of additional sources such configurations are shown to preserve half of the supersymmetries. Mirror symmetry relates the two sets of configurations. We discuss the implications for impurity models in 3d N=4 QED with a single charged hypermultiplet (and its mirror, the theory of a free hypermultiplet) as well as 3d N=2 QED with one flavor and its dual, a supersymmetric Wilson-Fisher fixed point. Mirror symmetry allows us to find backreacted solutions for arbitrary arrays of defects in the IR limit of N=4 QED. Our analysis, complemented with appropriate string theory brane constructions, sheds light on various aspects of mirror symmetry, the map between particles and vortices and the emergence of ground state entropy in QED at finite density.Comment: 33 pages, 10 figures. arXiv admin note: Figure 1 taken from arXiv:hep-th/970311

TTˉ+Λ2T\bar T + \Lambda_2 from a 2d gravity path integral

We develop a two-dimensional gravity path integral formulation of the $T \bar T + \Lambda_2$ deformation of quantum field theory. This provides an exactly solvable generalization of the pure $T \bar T$ deformation that is relevant for de Sitter and flat space holography. The path integral sheds light on quantum aspects of these flows in curved space, most notably the Weyl anomaly, the operator relation for the trace of the energy-momentum tensor, and the renormalization of the composite $T \bar T$ operator. It also applies to both the Hagedorn and the holographic signs of such flows. We present explicit calculations for the torus and sphere partition functions that reproduce previous results in the literature, now in path integral language. Finally, we use the path integral representation in order to establish an explicit map with 3d gravity, and obtain new predictions for flat space holography.Comment: 34 pages, 1 figur

Metallic quantum critical points with finite BCS couplings

We study the fate of superconductivity in the vicinity of a class of metallic quantum critical points obtained by coupling a Fermi surface to a critical boson. In such systems there is a competition between the enhanced pairing tendency due to the presence of long-range attractive interactions near criticality, and the suppression of superconductivity due to the destruction of the Landau quasiparticles. We show that there are regimes in which these two effects offset one another, resulting in a novel non-Fermi liquid fixed point with finite, scale invariant, BCS coupling. While these interactions lead to substantial superconducting fluctuations, they do not drive the system into a superconducting ground state. The metallic quantum critical fixed points are connected to the superconducting regime by a continuous phase transition. These results are established using a controlled expansion in the deviation from d=3 spatial dimensions, as well as in a large number N of internal flavors. We discuss the possible relevance of our findings to the phenomenon of superconducting domes condensing out of a non-Fermi liquid normal state near quantum critical points.Comment: 28 pages, 7 figure

Holographic RG flows, entanglement entropy and the sum rule

We calculate the two-point function of the trace of the stress tensor in holographic renormalization group flows between pairs of conformal field theories. We show that the term proportional to the momentum squared in this correlator gives the change of the central charge between fixed points in d=2 and in d>2 it gives the holographic entanglement entropy for a planar region. This can also be seen as a holographic realization of the Adler-Zee formula for the renormalization of Newton's constant. Holographic regularization is found to provide a perfect match of the finite and divergent terms of the sum rule, and it is analogous to the regularization of the entropy in terms of mutual information. Finally, we provide a general proof of reflection positivity in terms of stability of the dual bulk action, and discuss the relation between unitarity constraints, the null energy condition and regularity in the interior of the gravity solution.Comment: v2: 32 pages, 1 figure. Refs. and comments added. Version published in JHE

The g-theorem and quantum information theory

We study boundary renormalization group flows between boundary conformal field theories in $1+1$ dimensions using methods of quantum information theory. We define an entropic $g$-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this $g$-function decreases along boundary renormalization group flows. This entropic $g$-theorem is valid at zero temperature, and is independent from the $g$-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.Comment: 34 pages + appendices, 8 figures. v2. Improved and corrected version of the proo