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Andreas Karch

Publications and source records attributed to Andreas Karch.

At least 73 records · Page 4Linked to original sources
arXiv2017

Bosonizing three-dimensional quiver gauge theories

We start with the recently conjectured 3d bosonization dualities and gauge global symmetries to generate an infinite sequence of new dualities. These equate theories with non-Abelian product gauge groups and bifundamental matter. We uncover examples of Bose/Bose and Fermi/Fermi dualities, as well as a sequence of dualities between theories with scalar matter in two-index representations. Our conjectures are consistent with level/rank duality in massive phases.

hep-th↗
arXiv2017

Magnetoresistance in relativistic hydrodynamics without anomalies

We present expressions for the magnetoconductivity and the magnetoresistance of a strongly interacting metal in 3+1 dimensions, derivable from relativistic hydrodynamics. Such an approach is suitable for ultraclean metals with emergent Lorentz invariance. When this relativistic fluid contains chiral anomalies, it is known to exhibit longitudinal negative magnetoresistance. We show that similar effects can arise in non-anomalous relativistic fluids due to the distinctive gradient expansion. In contrast with a Galilean-invariant fluid, the resistivity tensor of a dirty relativistic fluid exhibits similar angular dependence to negative magnetoresistance, even when the constitutive relations and momentum relaxation rate are isotropic. We further account for the effect of magnetic field-dependent corrections to the gradient expansion and the effects of long-wavelength impurities on magnetoresistance. We note that the holographic D3/D7 system exhibits negative magnetoresistance.

hep-th↗
arXiv2017

Boundary Kinematic Space

We extend kinematic space to a simple scenario where the state is not fixed by conformal invariance: the vacuum of a conformal field theory with a boundary (bCFT). We identify the kinematic space associated with the boundary operator product expansion (bOPE) as a subspace of the full kinematic space. In addition, we establish representations of the corresponding bOPE blocks in a dual gravitational description. We show how the new kinematic dictionary and the dynamical data in bOPE allows one to reconstruct the bulk geometry. This is evidence that kinematic space may be a useful construction for understanding bulk physics beyond just kinematics.

hep-th↗
arXiv2016

Supersymmetric Adler Functions and Holography

We perform several tests on a recent proposal by Shifman and Stepanyantz for an exact expression for the current correlation functions in supersymmetric gauge theories. We clarify the meaning of the relation in superconformal theories. In particular we show that it automatically follows from known relations between the current correlation functions and anomalies. It therefore also automatically matches between different dual realizations of the same superconformal theory. We use holographic examples as well as calculations in free theories to show that the proposed relation fails in theories with mass terms.

hep-th↗
arXiv2016

Particle-Vortex Duality from 3d Bosonization

We provide a simple derivation of particle-vortex duality in d=2+1 dimensions. Our starting point is a relativistic form of flux attachment, designed to transmute the statistics of particles. From this seed, we derive a web of new dualities. These include particle-vortex duality for bosons as well as the recently discovered counterpart for fermions.

hep-th↗
arXiv2015

Unparticles and Anomalous Dimensions in the Cuprates

Motivated by the overwhelming evidence some type of quantum criticality underlies the power-law for the optical conductivity and $T-$linear resistivity in the cuprates, we demonstrate here how a scale-invariant or unparticle sector can lead to a unifying description of the observed scaling forms. We adopt the continuous mass formalism or multi band (flavor) formalism of the unparticle sector by letting various microscopic parameters be mass-dependent. In particular, we show that an effective mass that varies with the flavor index as well as a running band edge and lifetime capture the AC and DC transport phenomenology of the cuprates. A key consequence of the running mass is that the effective dynamical exponent can differ from the underlying bare critical exponent, thereby providing a mechanism for realizing the fractional values of the dynamical exponent required in a previous analysis\cite{ Hartnoll:2015sea}. We also predict that regardless of the bare dynamical exponent, $z$, a non-zero anomalous dimension for the current is required. Physically, the anomalous dimension arises because the charge depends on the flavor, mass or energy. The equivalent phenomenon in a $d+1$ gravitational construction is the running of the charge along the radial direction. The nature of the superconducting instability in the presence of scale invariant stuff shows that the transition temperature is not necessarily a monotonic function of the pairing interaction.

cond-mat.str-el↗
arXiv2015

Holographic Black Hole Chemistry

Thermodynamic quantities associated with black holes in Anti-de Sitter space obey an interesting identity when the cosmological constant is included as one of the dynamical variables, the generalized Smarr relation. We show that this relation can easily be understood from the point of view of the dual holographic field theory. It amounts to the simple statement that the extensive thermodynamic quantities of a large $N$ gauge theory only depend on the number of colors, $N$, via an overall factor of $N^2$.

hep-th↗
arXiv2015

Spinor fields in general Newton-Cartan backgrounds

We give a covariant construction of Lagrangians for spinor fields in generic Newton-Cartan backgrounds. A non-relativistic Dirac/Levy-Leblond operator and the associated fields are obtained from relativistic analogues by a limiting procedure. The relativistic symmetries induce the complete set of non-relativistic symmetries, including Milne boosts and local Galilean transformations. The resulting Levy-Leblond operator includes non-minimal couplings to the Newton-Cartan structure as well as to the gauge field, and with these couplings it transforms covariantly. Phenomenologically, this fixes the gyromagnetic ratio to g=1. Three-dimensional spacetimes are an exception: generic g is possible but results in modified Milne transformations, which - upon gauge fixing - reproduces the anomalous diffeomorphisms found in earlier approaches.

hep-th↗
arXiv2015

A Precision Test of AdS/CFT with Flavor

In this letter we put AdS/CFT dualities involving probe branes to a precision test. On the holographic side we use a new class of supersymmetric D7-brane embeddings into AdS$_5\times$S$^5$, which allow to describe N=4 SYM coupled to massive N=2 supersymmetric flavors on S$^4$. With these embeddings we can compare holographic results to a field theory analysis of the free energy using supersymmetric localization. Localization allows us to get results at strong coupling, and hence to compare in detail to AdS/CFT. We find analytically matching results: a phase transition at the same critical mass in both calculations and matching free energies up to a scheme-dependent constant in both phases.

hep-th↗
arXiv2015

Supersymmetric D3/D7 for holographic flavors on curved space

We derive a new class of supersymmetric D3/D7 brane configurations, which allow to holographically describe N=4 SYM coupled to massive N=2 flavor degrees of freedom on spaces of constant curvature. We systematically solve the $κ$-symmetry condition for D7-brane embeddings into AdS$_4$-sliced AdS$_5\times$S$^5$, and find supersymmetric embeddings in a simple closed form. Up to a critical mass, these embeddings come in surprisingly diverse families, and we present a first study of their (holographic) phenomenology. We carry out the holographic renormalization, compute the one-point functions and attempt a field-theoretic interpretation of the different families. To complete the catalog of supersymmetric D3/D7 configurations, we construct analogous embeddings for flavored N=4 SYM on S$^4$ and dS$_4$.

hep-th↗
arXiv2015

Multiband models for field theories with anomalous current dimension

We give simple examples of weakly coupled or free quantum mechanical systems that exhibit scale invariance with an anomalous dimension for a conserved current. In these models scaling as an exact symmetry only emerges in a large N limit, but it remains as an approximate symmetry even at finite N.

hep-th↗
arXiv2015

Towards a Holographic Bose-Hubbard Model

We present a holographic construction of the large-N Bose-Hubbard model. The model is based on Maxwell fields coupled to charged scalar fields on the AdS2 hard wall. We realize the lobe-shaped phase structure of the Bose-Hubbard model and find that the model admits Mott insulator ground states in the limit of large Coulomb repulsion. In the Mott insulator phases, the bosons are localized on each site. At zero hopping we find that the transitions between Mott insulating phases with different fillings correspond to first order level-crossing phase transitions. At finite hopping we find a holographic phase transition between the Mott phase and a non-homogeneous phase. We then analyze the perturbations of fields around both the Mott insulator phase and inhomogeneous phase. We find almost zero modes in the non-homogeneous phase.

hep-th↗
arXiv2015

Holographic entanglement entropy and the internal space

We elaborate on the role of extremal surfaces probing the internal space in AdS/CFT. Extremal surfaces in AdS quantify the "geometric" entanglement between different regions in physical space for the dual CFT. This, however, is just one of many ways to split a given system into subsectors, and extremal surfaces in the internal space should similarly quantify entanglement between subsectors of the theory. For the case of AdS$_5\times$S$^5$, their area was interpreted as entanglement entropy between U(n) and U(m) subsectors of U(n+m) N=4 SYM. Making this proposal precise is subtle for a number of reasons, the most obvious being that from the bulk one usually has access to gauge-invariant quantities only, while a split into subgroups is inherently gauge variant. We study N=4 SYM on the Coulomb branch, where some of the issues can be mitigated and the proposal can be sharpened. Continuing back to the original AdS$_5\times$S$^5$ geometry, we obtain a modified proposal, based on the relation of the internal space to the R-symmetry group.

hep-th↗
arXiv2015

Scaling theory of the cuprate strange metals

We show that the anomalous temperature scaling of five distinct transport quantities in the strange metal regime of the cuprate superconductors can be reproduced with only two nontrivial critical exponents. The quantities are: (i) the electrical resistivity, (ii) the Hall angle, (iii) the Hall Lorenz ratio, (iv) the magnetoresistance and (v) the thermopower. The exponents are the dynamical critical exponent z = 4/3 and an anomalous scaling dimension Phi = -2/3 for the charge density operator.

cond-mat.str-el↗
arXiv2014

Revisiting non-relativistic limits

We show that the full spurionic symmetry of Galilean-invariant field theories can be deduced when those theories are the limits of relativistic parents. Under the limit, the non-relativistic daughter couples to Newton-Cartan geometry together with all of the symmetries advocated in previous work, including the recently revived Milne boosts. Our limit is a covariant version of the usual one, where we start with a gapped relativistic theory with a conserved charge, turn on a chemical potential equal to the rest mass of the lightest charged state, and then zoom in to the low energy sector. This procedure gives a simple physical interpretation for the Milne boosts. Our methods even apply when there is a magnetic moment, which is known to modify the non-relativistic symmetry transformations. We focus on two examples, taking the non-relativistic limits of scalar field theory and hydrodynamics.

hep-th↗
arXiv2014

Flavored N=4 SYM -- a highly entangled quantum liquid

We study N=4 SYM theory coupled to fundamental N=2 hypermultiplets in a state of finite charge density. The setup can be described holographically as a configuration of D3 and D7 branes with a non-trivial worldvolume gauge field on the D7. The phase has been identified as a new form of quantum liquid, where certain properties are those of a Fermi liquid while others are clearly distinct. We focus on the entanglement among the flavors, as quantified by the entanglement entropy. The expectation for a Fermi liquid would be a logarithmic enhancement of the area law, but we find a more drastic enhancement instead. The leading contributions are volume terms with a non-trivial shape dependence, signaling extensive entanglement among the flavors. At finite temperature these correlations are confined to a region of size given by the inverse temperature.

hep-th↗
arXiv2014

Conductivities for Hyperscaling Violating Geometries

We show that many results about holographic conductivities in geometries with hyperscaling violating scaling can be reproduced from simple scaling laws in the dual field theory. We show that the electro-magnetic response of probe branes in these systems require at least one additional scaling parameter Phi beyond the usual dynamical exponent z and hyperscaling violating exponent theta, as also pointed out in earlier work. We show that the scaling exponents can be chosen in such a way that the temperature dependence of DC conductivity and Hall angle in strange metals can be reproduced.

hep-th↗