The transport properties of dense QCD matter play a crucial role in the physics of neutron stars and their mergers but are notoriously difficult to study with traditional quantum field theory tools. Specializing to the case of unpaired quark matter in beta equilibrium, we approach the problem through the machinery of holography, in particular the V-QCD and D3-D7 models, and derive results for the electrical and thermal conductivities and the shear and bulk viscosities. In addition we compare the bulk to shear viscosity ratio to the speed of sound and find that it violates the so-called Buchel bound. Our results differ dramatically from earlier predictions of perturbative QCD, the root causes and implications of which we analyze in detail.

Spain

Carlos Hoyos

Finland

Niko Jokela

South Korea

Matti Järvinen

Sweden

Javier G. Subils

Javier Tarrío

Aleksi Vuorinen

Holographic approach to transport in dense QCD matter

Energy conditions, especially the null energy condition (NEC), are generically imposed on solutions to retain a physically sensible classical field theory and they also play an important role in the AdS/CFT duality. Using this duality, we study non-trivially deformed strongly coupled quantum field theories at large-N  c . The corresponding dual classical gravity constructions entail the use of radially non-monotonic D-brane distributions. The distributions are phenomenological in the sense that they do not correspond to the smearing of known probe D-brane embeddings. The gravity backgrounds are supersymmetric and hence perturbatively stable, and do not possess curvature singularities. There are no short-cuts through the bulk spacetime for signal propagation which assures that the field theory duals are causal. Nevertheless, some of our solutions violate the NEC in the gravity dual. In these cases the non-monotonicity of the D-brane distributions is reflected in the properties of the renormalization group flow: none of the c-functions proposed in the literature are monotonic. This further suggests that the non-monotonic behavior of the c-functions within previously known anisotropic backgrounds does not originate from the breaking of Lorentz invariance. We surmise that NEC violations induced by quantum corrections also need to be considered in holographic duals, but can be studied already at the classical level.

United Kingdom

José Penín

Alfonso Ramallo

Risking your NEC

Motivated by the possible presence of deconfined quark matter in neutron stars and their mergers and the important role of transport phenomena in these systems, we perform the first-ever systematic study of different viscosities and conductivities of dense quark matter using the gauge/gravity duality. Using the V-QCD model, we arrive at results that are in qualitative disagreement with the predictions of perturbation theory, which highlights the differing transport properties of the system at weak and strong coupling and calls for caution in the use of the perturbative results in neutron star applications.

Israel

Transport in Strongly Coupled Quark Matter

We classify the non-supersymmetric, and perturbatively stable within D = 4, AdS vacua of maximal D = 4 supergravity with a dyonic ISO(7) gauging in a large sector of the supergravity. Seven such vacua are established within this sector, all of them giving rise to non-supersymmetric AdS4 × S6 type IIA backgrounds with and without non-trivial warpings and with internal fluxes. Then, we analyse the dynamics of various probe Dp- branes in these backgrounds searching for potential brane-jet instabilities. In all these cases, such instabilities are absent. Finally, an alternative decay channel through tunnelling is investigated, focusing on one of the seven backgrounds. We do not find instabilities either, but the analysis remains inconclusive.

Adolfo Guarino

United States

Oscar Varela

Brane-jet stability of non-supersymmetric AdS vacua

New renormalisation group flows of three-dimensional Chern-Simons theories with a single gauge group SU(N ) and adjoint matter are found holographically. These RG flows have an infrared fixed point given by a CFT with   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 supersymmetry and SU(2) flavour symmetry. The ultraviolet fixed point is again described by a CFT with either   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 and SU(3) symmetry or   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 and G2 symmetry. The gauge/gravity duals of these RG flows are constructed as domain-wall solutions of a gauged supergravity model in four dimensions that enjoys an embedding into massive IIA supergravity. A concrete RG flow that brings a mass deformation of the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 CFT into the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 CFT at low energies is described in detail.

Flowing to   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 Chern-Simons-matter theory

We have identified a sign in our paper that needed to be corrected. The main conclusion of our paper was the presence of instabilities that suggest the existence of crystalline phases in the system.

Antón Faedo

David Mateos

Christiana Pantelidou

Belgium

Erratum to: Towards a holographic quark matter crystal

Half-maximal,   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4, sectors of D = 4   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 8 supergravity with a dyonic ISO(7) gauging are investigated. We focus on a half-maximal sector including three vector multiplets, that arises as a certain SO(3)R-invariant sector of the full theory. We discuss the embedding of this sector into the largest half-maximal sector of the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 8 supergravity retaining six vector multiplets. We also provide its canonical   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 formulation and show that, from this perspective, our model leads in its own right to a new explicit gauging of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 supergravity. Finally, expressions for the restricted duality hierarchy are given and the vacuum structure is investigated. Five new non-supersymmetric AdS vacua are found numerically. The previously known   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 and   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 AdS vacua are also contained in our   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 model. Unlike when embedded in previously considered sectors with fewer fields, these vacua exhibit their full   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 and   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 supersymmetry within our   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 model.

Halving ISO(7) supergravity

We have recently shown that the ground state of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4, SU(N c) super Yang- Mills coupled to N f ≪ N c flavors, in the presence of non-zero isospin and R-symmetry charges, is a supersymmetric, superfluid, color superconductor. The holographic description consists of N f D7-brane probes in AdS5 ×S5 with electric and instantonic fields on their worldvolume. These correspond to fundamental strings and D3-branes dissolved on the D7-branes, respectively. Here we use this description to determine the spectrum of mesonic excitations. As expected for a charged superfluid we find non-relativistic, massless Goldstone modes. We also find extra ungapped modes that are not associated to the breaking of any global symmetries but to the supersymmetric nature of the ground state. If the quark mass is much smaller than the scale of spontaneous symmetry breaking a pseudo-Goldstone boson is also present. We highlight some new features that appear only for N f &gt; 2. We show that, in the generic case of unequal R-symmetry charges, the dissolved strings and D3-branes blow up into a D5-brane supertube stretched between the D7-branes.

Spectrum of a supersymmetric color superconductor

We use holography to study d = 4,   <math> <mi>N</mi> <mo>=</mo> <mn>4</mn> </math>  $$ \mathcal{N}=4 $$ , SU(N c) super Yang-Mills coupled to N f ≪ N c quark flavors. We place the theory at finite isospin density n I by turning on an isospin chemical potential μ I = M q, with M q the quark mass. We also turn on two R-symmetry charge densities n 1 = n 2. We show that the ground state is a supersymmetric, superfluid, color superconductor, namely a finite-density state that preserves a fraction of supersymmetry in which part of the global symmetries and part of the gauge symmetries are spontaneously broken. The holographic description consists of N f D7-brane probes in AdS5 × S5. The symmetry breaking is due to the dissolution of some D3-branes inside the D7-branes triggered by the electric field associated to the isospin charge. The massless spectrum contains Goldstone bosons and their fermionic superpartners. The massive spectrum contains long-lived, mesonic quasi-particles if n I ≪ μ  I 3 , and no quasi-particles otherwise. We discuss the possibility that, despite the presence of mass scales and charge densities in the theory, conformal and relativistic invariance arise as emergent symmetries in the infrared.

A supersymmetric color superconductor from holography

The dynamics of surfaces and interfaces describe many physical systems, including fluid membranes, entanglement entropy and the coupling of defects to quantum field theories. Based on the formulation of submanifold calculus developed by Carter, we introduce a new variational principle for (entangling) surfaces. This principle captures all diffeomorphism constraints on surface/interface actions and their associated spacetime stress tensor. The different couplings to the geometric tensors appearing in the surface action are interpreted in terms of response coefficients within elasticity theory. An example of a surface action with edges at the two-derivative level is studied, including both the parity-even and parity-odd sectors. Its conformally invariant counterpart restricts the type of conformal anomalies that can appear in two-dimensional submanifolds with boundaries. Analogously to hydrodynamics, it is shown that classification methods can be used to constrain the stress tensor of (entangling) surfaces at a given order in derivatives. This analysis reveals a purely geometric parity-odd contribution to the Young modulus of a thin elastic membrane. Extending this novel variational principle to BCFTs and DCFTs in curved spacetimes allows to obtain the Ward identities for diffeomorphism and Weyl transformations. In this context, we provide a formal derivation of the contact terms in the stress tensor and of the displacement operator for a broad class of actions.