arXiv subjects

Gonzalo Torroba

Publications and source records attributed to Gonzalo Torroba.

At least 55 records · Page 3Linked to original sources

arXiv2016

Bosonization and Mirror Symmetry

We study bosonization in 2+1 dimensions using mirror symmetry, a duality that relates pairs of supersymmetric theories. Upon breaking supersymmetry in a controlled way, we dynamically obtain the bosonization duality that equates the theory of a free Dirac fermion to QED3 with a single scalar boson. This duality may be used to demonstrate the bosonization duality relating an $O(2)$-symmetric Wilson-Fisher fixed point to QED3 with a single Dirac fermion, Peskin-Dasgupta-Halperin duality, and the recently conjectured duality relating the theory of a free Dirac fermion to fermionic QED3 with a single flavor. Chern-Simons and BF couplings for both dynamical and background gauge fields play a central role in our approach. In the course of our study, we describe a chiral mirror pair that may be viewed as the minimal supersymmetric generalization of the two bosonization dualities.

hep-th↗

arXiv2016

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.

hep-th↗

arXiv2016

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.

hep-th↗

arXiv2015

Mirror symmetry and the half-filled Landau level

We study the dynamics of the half-filled zeroth Landau level of Dirac fermions using mirror symmetry, a supersymmetric duality between certain pairs of $2+1$-dimensional theories. We show that the half-filled zeroth Landau level of a pair of Dirac fermions is dual to a pair of Fermi surfaces of electrically-neutral composite fermions, coupled to an emergent gauge field. Thus, we use supersymmetry to provide a derivation of flux attachment and the emergent Fermi liquid-like state for the lowest Landau level of Dirac fermions. We find that in the dual theory the Coulomb interaction induces a dynamical exponent $z=2$ for the emergent gauge field, making the interactions classically marginal. This enables us to map the problem of $2+1$-dimensional Dirac fermions in a finite transverse magnetic field, interacting via a strong Coulomb interaction, into a perturbatively controlled model. We analyze the resulting low-energy theory using the renormalization group and determine the nature of the BCS interaction in the emergent composite Fermi liquid.

cond-mat.str-el↗

arXiv2015

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.

cond-mat.str-el↗

arXiv2015

Enhanced Pairing of Quantum Critical Metals Near d=3+1

We study the dynamics of a quantum critical boson coupled to a Fermi surface in intermediate energy regimes where the Landau damping of the boson can be parametrically controlled, either via large Fermi velocity or by large N techniques. We focus on developing a systematic approach to studying the BCS instability, including careful treatment of the enhanced log^2 and log^3 singularities which appear already at 1-loop. We also treat possible instabilities to charge density wave (CDW) formation, and compare the scales Lambda_{BCS} and Lambda_{CDW} of the onset of the instabilities in different parametric regimes. We address the question of whether the dressing of the fermions into a non-Fermi liquid via interactions with the order parameter field can happen at energies > Lambda_{BCS}, Lambda_{CDW}.

cond-mat.str-el↗

arXiv2015

Aspects of Renormalization in Finite Density Field Theory

We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction "Landau parameters" run already at tree level. Our explicit one loop analysis resolves previously found obstacles in the renormalization of finite density field theory, including logarithmic divergences in non-local interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of $2 k_F$ singularities, and a companion paper considers the RG for Fermi surface instabilities. We end with some comments on the renormalization of finite density field theory with the inclusion of Landau damping of the boson.

cond-mat.str-el↗

arXiv2014

Quantum critical metals in $4-ε$ dimensions

We study the quantum theory of a Fermi surface coupled to a gapless boson scalar in $D=4-ε$ 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 $ω^ε$ 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 $ε$--expansion.

cond-mat.str-el↗

arXiv2014

New solutions with accelerated expansion in string theory

We present concrete solutions with accelerated expansion in string theory, requiring a small, tractable list of stress energy sources. We explain how this construction (and others in progress) evades previous no go theorems for simple accelerating solutions. Our solutions respect an approximate scaling symmetry and realize discrete sequences of values for the equation of state, including one with an accumulation point at w=-1 and another accumulating near w=-1/3 from below. In another class of models, a density of defects generates scaling solutions with accelerated expansion. We briefly discuss potential applications to dark energy phenomenology, and to holography for cosmology.

hep-th↗

arXiv2014

Emergent Fermi surfaces, fractionalization and duality in supersymmetric QED

We study the physics of 3d supersymmetric abelian gauge theories (with small supersymmetry breaking perturbations) at finite density. Using mirror symmetry, which provides a natural generalization of the duality between the XY model and the abelian Higgs model but now including fermionic fields, we see many dynamical phenomena conjectured to be of relevance in condensed matter systems. In particular, we find examples of the emergence of a Fermi surface at low energies from hybridization of fermions localized at magnetic defects at high energies, as well as fractionalization of charged fermions into spinon-holon pairs with the concomitant appearance of emergent gauge fields. We also find dual descriptions for Fermi surfaces coupled to critical bosons, which give rise to non-Fermi liquids.

hep-th↗

arXiv2014

Exploring eternal stability with the simple harmonic universe

We construct nonsingular cyclic cosmologies that respect the null energy condition, have a large hierarchy between the minimum and maximum size of the universe, and are stable under linearized fluctuations. The models are supported by a combination of positive curvature, a negative cosmological constant, cosmic strings and matter that at the homogeneous level behaves as a perfect fluid with equation of state -1 < w < -1/3. We investigate analytically the stability of the perturbation equations and discuss the role of parametric resonances and nonlinear corrections. Finally, we argue that Casimir energy contributions associated to the compact spatial slices can become important at short scales and lift nonperturbative decays towards vanishing size. This class of models (particularly in the static limit) can then provide a useful framework for studying the question of the ultimate (meta)stability of an eternal universe.

hep-th↗

arXiv2014

Controlled non-Fermi liquids from spacetime dependent couplings

We construct perturbatively controlled non-Fermi liquids in 3+1 spacetime dimensions, using mild power-law translation breaking interactions. Our mechanism balances the leading tree level effects from such gradients against quantum effects from the interaction between the Fermi surface and a critical boson. We exhibit this in a model where finite density fermions interact with a scalar field via a Yukawa coupling of the form $g(x)\propto |x|^κ$. The approximate non-Fermi liquid behavior arises in the limit of small $κ$ and persists over an exponentially large window of scales, being cut off by the regime where the coupling becomes large, or by superconducting instabilities. The translation breaking coupling introduces anisotropic deformations of the Fermi surface depending on the direction of the gradient. An extension of this mechanism to 2+1 dimensions could provide a strongly translation-breaking, but weakly coupled non-fermi liquid, something we leave for further work.

cond-mat.str-el↗

arXiv2014

A Simple Harmonic Universe

We explore simple but novel bouncing solutions of general relativity that avoid singularities. These solutions require curvature k=+1, and are supported by a negative cosmological term and matter with -1 < w < -1/3. In the case of moderate bounces (where the ratio of the maximal scale factor $a_+$ to the minimal scale factor $a_-$ is ${\cal O}(1)$), the solutions are shown to be classically stable and cycle through an infinite set of bounces. For more extreme cases with large $a_+/a_-$, the solutions can still oscillate many times before classical instabilities take them out of the regime of validity of our approximations. In this regime, quantum particle production also leads eventually to a departure from the realm of validity of semiclassical general relativity, likely yielding a singular crunch. We briefly discuss possible applications of these models to realistic cosmology.

hep-th↗

arXiv2013

S-duality of nonsupersymmetric gauge theories

We propose a method for constructing pairs of nonsupersymmetric gauge theories related by S-duality. Starting from a known S-duality of supersymmetric theories realized on the worldvolume of D3 branes in type IIB string theory, a new duality is obtained by replacing the D3-branes with antibranes. Large classes of dual pairs of nonsupersymmetric theories can be obtained in this way, with different interactions and matter content (chiral and vector-like). The approach is illustrated on gauge theories realized on three-branes and fractional branes probing orbifold singularities. The duality sheds light on the dynamics of gauge theories and their possible infrared phases by providing concrete magnetic dual descriptions of strongly coupled theories. Some of the models share various properties with QCD, including confinement and chiral symmetry breaking. More generally, these theories feature fermions in multiple two-index representations and could realize intriguing phases such as a free magnetic phase with chiral symmetry breaking or mixed phases where an interacting fixed point coexists with a confining phase.

hep-th↗

arXiv2013

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.

hep-th↗

arXiv2013

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.

hep-th↗

arXiv2013

Moduli Stabilization and the Holographic RG for AdS and dS

We relate moduli stabilization ($V'=0$) in the bulk of $AdS_D$ or $dS_D$ to basic properties of the Wilsonian effective action in the holographic dual theory on $dS_{D-1}$: the single-trace terms in the action have vanishing beta functions, and higher-trace couplings are determined purely from lower-trace ones. In the de Sitter case, this encodes the maximal symmetry of the bulk spacetime in a quantity which is accessible within an observer patch. Along the way, we clarify the role of counterterms, constraints, and operator redundancy in the Wilsonian holographic RG prescription, reproducing the expected behavior of the trace of the stress-energy tensor in the dual for both $AdS_D$ and $dS_D$. We further show that metastability of the gravity-side potential energy corresponds to a nonperturbatively small imaginary contribution to the Wilsonian action of pure de Sitter, a result consistent with the need for additional degrees of freedom in the holographic description of its ultimate decay.

hep-th↗

arXiv2013

Topological resolution of gauge theory singularities

Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high energy metric (that would exhibit the singularity) and a regular singularity-free low energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.

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