We test the proposal of [1] for the holographic computation of the charged moments and the result... more We test the proposal of [1] for the holographic computation of the charged moments and the resulting symmetry-resolved entanglement entropy in different excited states, as well as for two entangling intervals. Our holographic computations are performed in U(1) Chern-Simons-Einstein-Hilbert gravity, and are confirmed by independent results in a conformal field theory at large central charge. In particular, we consider two classes of excited states, corresponding to charged and uncharged conical defects in AdS3. In the conformal field theory, these states are generated by the insertion of charged and uncharged heavy operators. We employ the monodromy method to calculate the ensuing four-point function between the heavy operators and the twist fields. For the two-interval case, we derive our results on the AdS and the conformal field theory side, respectively, from the generating function method of [1], as well as the vertex operator algebra. In all cases considered, we find equipartit...
A holographic large-N Bose-Hubbard model has been presented in arXiv:1411.7899[hep-th]. The holog... more A holographic large-N Bose-Hubbard model has been presented in arXiv:1411.7899[hep-th]. The holographic model is a theory with Maxwell fields and charged scalar fields on the AdS2 hard wall. The lobe-shaped phase structure of the Bose-Hubbard model is realized by using holography. The Mott insulator phase in which bosons are localized on each site is found for large repulsive interaction. In addition to the phase transition between Mott insulator phases with different occupation numbers at zero hopping integral, a holographic phase transition is found at non-zero hopping integral between the Mott insulator phase and a non-homogeneous phase. The perturbations of fields are also analyzed around both the Mott insulator phase and the non-homogeneous phase. Almost zero modes are found in the non-homogeneous phase.
A current challenge in condensed matter physics is the realization of strongly correlated, viscou... more A current challenge in condensed matter physics is the realization of strongly correlated, viscous electron fluids. These fluids can be described by holography, that is, by mapping them onto a weakly curved gravitational theory via gauge/gravity duality. The canonical system considered for realizations has been graphene. In this work, we show that Kagome systems with electron fillings adjusted to the Dirac nodes provide a much more compelling platform for realizations of viscous electron fluids, including non-linear effects such as turbulence. In particular, we find that in Scandium Herbertsmithite, the fine-structure constant, which measures the effective Coulomb interaction, is enhanced by a factor of about 3.2 as compared to graphene. We employ holography to estimate the ratio of the shear viscosity over the entropy density in Sc-Herbertsmithite, and find it about three times smaller than in graphene. These findings put the turbulent flow regime described by holography within the...
Abstract: We investigate gauge/gravity duals with flavour for which pure-gauge Kalb-Ramond B fiel... more Abstract: We investigate gauge/gravity duals with flavour for which pure-gauge Kalb-Ramond B fields are turned on in the background, into which a D7 brane probe is embedded. First we consider the case of a magnetic field in two of the spatial boundary directions. We show that at finite temperature, i.e. in the AdS-Schwarzschild background, the B field has a stabilizing effect on the mesons and chiral symmetry breaking occurs for a sufficiently large value of the B field. Then we turn to the electric case of a B field in the temporal direction and one spatial boundary direction. In this case, there is a singular region in which it is necessary to turn on a gauge field on the brane in order to ensure reality of the brane action. We find that the brane embeddings are attracted towards this region. Far away from this region, in the weak field case at zero temperature, we investigate the meson spectrum and find a mass shift similar to the Stark effect. Keywords: AdS-CFT correspondence, B...
Key words AdS/CFT, holography, charged dilatonic black holes, strange metals, Mott insulator. We ... more Key words AdS/CFT, holography, charged dilatonic black holes, strange metals, Mott insulator. We review a recent holographic analysis [1] of charged black holes with scalar hair in view of their ap-plications to the cuprate high temperature superconductors. We show in particular that these black holes show an interesting phase structure including critical behaviour at zero temperature or charge, describe both conductors and insulators (including holographic Mott-like insulators), generically have no residual entropy and exhibit experimentally observed scaling relations between electronic entropy, specific heat and (linear) DC resistivity. Transport properties are discussed in the companion contribution [2] in these proceedings. Copyright line will be provided by the publisher 1
A non-technical overview on gravity in two dimensions is provided. Applications discussed in this... more A non-technical overview on gravity in two dimensions is provided. Applications discussed in this work comprise 2D type 0A/0B string theory, Black Hole evaporation/thermodynamics, toy models for quantum gravity, for numerical General Relativity in the context of critical collapse and for solid state analogues of Black Holes. Mathematical relations to integrable models, non-linear gauge theories, Poisson-sigma models, KdV surfaces and non-commutative geometry are presented. Key Words: Black Holes in String Theory, 2D Gravity, Integrable Models. 1.
I am deeply indebted to Dr. Daniel Grumiller who, with much patience, guided me in my scientific ... more I am deeply indebted to Dr. Daniel Grumiller who, with much patience, guided me in my scientific work while at the same time always having an open ear for my questions. I also want to thank Prof. Dr. Gerd Rudolph for taking responsibility for the official supervision of this thesis, for friendly welcoming me in his research group and for the interest he expressed towards the topic of this thesis. Furthermore, I am grateful to Dr. Dmitri Vassilevich for his constant scientific and non-scientific advice and for many stimulating comments and discussions. My parents deserve every thank for the support they gave me in times which were far from being easy for themselves, as well as my wife, whose love is a constant source of strength and encouragement for me. Thanks also go to all my friends for the good times we had during our studies and for helping and supporting me in every manner. Last but not least I am very grateful to the German National Academic Foundation, whose scholarship enab...
We study the time development of strongly coupled ${\cal N}=4$ supersymmetric Yang Mills (SYM) th... more We study the time development of strongly coupled ${\cal N}=4$ supersymmetric Yang Mills (SYM) theory on cosmological Friedmann-Robertson-Walker (FRW) backgrounds via the AdS/CFT correspondence. We implement the cosmological background as a boundary metric fulfilling the Friedmann equation with a four-dimensional cosmological constant and a dark radiation term. We analyze the dual bulk solution of the type IIB supergravity and find that the time-dependence of the FRW background strongly influences the dynamical properties of the SYM theory. We in particular find a phase transition between a confined and a deconfined phase. We also argue that some cosmological solutions could be related to the inflationary scenario.
In this paper, we analyze a proposed gravity dual to a SU(N) Bose-Hubbard model, as well as const... more In this paper, we analyze a proposed gravity dual to a SU(N) Bose-Hubbard model, as well as construct a holographic dual of a SU(N) Fermi-Hubbard model from D-branes in string theory. In both cases, the SU(N) is dynamical, i.e. the hopping degrees of freedom are strongly coupled to SU(N) gauge bosons which themselves are strongly interacting. The vacuum expectation value (VEV) of the hopping term (i.e. the hopping energy) is analyzed in the gravity dual as a function of the bulk mass of the field dual to the hopping term, as well as of the coupling constants of the model. The bulk mass controls the anomalous dimension (i.e. the critical exponent) of the hopping term in the SU(N) Bose-Hubbard model. We compare the hopping energy to the corresponding result in a numerical simulation of the ungauged SU(N ) Bose-Hubbard model. We find agreement when the hopping parameter is smaller than the other couplings. Our analysis shows that the kinetic energy increases as the bulk mass increases,...
We test the proposal of [1] for the holographic computation of the charged moments and the result... more We test the proposal of [1] for the holographic computation of the charged moments and the resulting symmetry-resolved entanglement entropy in different excited states, as well as for two entangling intervals. Our holographic computations are performed in U(1) Chern-Simons-Einstein-Hilbert gravity, and are confirmed by independent results in a conformal field theory at large central charge. In particular, we consider two classes of excited states, corresponding to charged and uncharged conical defects in AdS3. In the conformal field theory, these states are generated by the insertion of charged and uncharged heavy operators. We employ the monodromy method to calculate the ensuing four-point function between the heavy operators and the twist fields. For the two-interval case, we derive our results on the AdS and the conformal field theory side, respectively, from the generating function method of [1], as well as the vertex operator algebra. In all cases considered, we find equipartit...
A holographic large-N Bose-Hubbard model has been presented in arXiv:1411.7899[hep-th]. The holog... more A holographic large-N Bose-Hubbard model has been presented in arXiv:1411.7899[hep-th]. The holographic model is a theory with Maxwell fields and charged scalar fields on the AdS2 hard wall. The lobe-shaped phase structure of the Bose-Hubbard model is realized by using holography. The Mott insulator phase in which bosons are localized on each site is found for large repulsive interaction. In addition to the phase transition between Mott insulator phases with different occupation numbers at zero hopping integral, a holographic phase transition is found at non-zero hopping integral between the Mott insulator phase and a non-homogeneous phase. The perturbations of fields are also analyzed around both the Mott insulator phase and the non-homogeneous phase. Almost zero modes are found in the non-homogeneous phase.
A current challenge in condensed matter physics is the realization of strongly correlated, viscou... more A current challenge in condensed matter physics is the realization of strongly correlated, viscous electron fluids. These fluids can be described by holography, that is, by mapping them onto a weakly curved gravitational theory via gauge/gravity duality. The canonical system considered for realizations has been graphene. In this work, we show that Kagome systems with electron fillings adjusted to the Dirac nodes provide a much more compelling platform for realizations of viscous electron fluids, including non-linear effects such as turbulence. In particular, we find that in Scandium Herbertsmithite, the fine-structure constant, which measures the effective Coulomb interaction, is enhanced by a factor of about 3.2 as compared to graphene. We employ holography to estimate the ratio of the shear viscosity over the entropy density in Sc-Herbertsmithite, and find it about three times smaller than in graphene. These findings put the turbulent flow regime described by holography within the...
Abstract: We investigate gauge/gravity duals with flavour for which pure-gauge Kalb-Ramond B fiel... more Abstract: We investigate gauge/gravity duals with flavour for which pure-gauge Kalb-Ramond B fields are turned on in the background, into which a D7 brane probe is embedded. First we consider the case of a magnetic field in two of the spatial boundary directions. We show that at finite temperature, i.e. in the AdS-Schwarzschild background, the B field has a stabilizing effect on the mesons and chiral symmetry breaking occurs for a sufficiently large value of the B field. Then we turn to the electric case of a B field in the temporal direction and one spatial boundary direction. In this case, there is a singular region in which it is necessary to turn on a gauge field on the brane in order to ensure reality of the brane action. We find that the brane embeddings are attracted towards this region. Far away from this region, in the weak field case at zero temperature, we investigate the meson spectrum and find a mass shift similar to the Stark effect. Keywords: AdS-CFT correspondence, B...
Key words AdS/CFT, holography, charged dilatonic black holes, strange metals, Mott insulator. We ... more Key words AdS/CFT, holography, charged dilatonic black holes, strange metals, Mott insulator. We review a recent holographic analysis [1] of charged black holes with scalar hair in view of their ap-plications to the cuprate high temperature superconductors. We show in particular that these black holes show an interesting phase structure including critical behaviour at zero temperature or charge, describe both conductors and insulators (including holographic Mott-like insulators), generically have no residual entropy and exhibit experimentally observed scaling relations between electronic entropy, specific heat and (linear) DC resistivity. Transport properties are discussed in the companion contribution [2] in these proceedings. Copyright line will be provided by the publisher 1
A non-technical overview on gravity in two dimensions is provided. Applications discussed in this... more A non-technical overview on gravity in two dimensions is provided. Applications discussed in this work comprise 2D type 0A/0B string theory, Black Hole evaporation/thermodynamics, toy models for quantum gravity, for numerical General Relativity in the context of critical collapse and for solid state analogues of Black Holes. Mathematical relations to integrable models, non-linear gauge theories, Poisson-sigma models, KdV surfaces and non-commutative geometry are presented. Key Words: Black Holes in String Theory, 2D Gravity, Integrable Models. 1.
I am deeply indebted to Dr. Daniel Grumiller who, with much patience, guided me in my scientific ... more I am deeply indebted to Dr. Daniel Grumiller who, with much patience, guided me in my scientific work while at the same time always having an open ear for my questions. I also want to thank Prof. Dr. Gerd Rudolph for taking responsibility for the official supervision of this thesis, for friendly welcoming me in his research group and for the interest he expressed towards the topic of this thesis. Furthermore, I am grateful to Dr. Dmitri Vassilevich for his constant scientific and non-scientific advice and for many stimulating comments and discussions. My parents deserve every thank for the support they gave me in times which were far from being easy for themselves, as well as my wife, whose love is a constant source of strength and encouragement for me. Thanks also go to all my friends for the good times we had during our studies and for helping and supporting me in every manner. Last but not least I am very grateful to the German National Academic Foundation, whose scholarship enab...
We study the time development of strongly coupled ${\cal N}=4$ supersymmetric Yang Mills (SYM) th... more We study the time development of strongly coupled ${\cal N}=4$ supersymmetric Yang Mills (SYM) theory on cosmological Friedmann-Robertson-Walker (FRW) backgrounds via the AdS/CFT correspondence. We implement the cosmological background as a boundary metric fulfilling the Friedmann equation with a four-dimensional cosmological constant and a dark radiation term. We analyze the dual bulk solution of the type IIB supergravity and find that the time-dependence of the FRW background strongly influences the dynamical properties of the SYM theory. We in particular find a phase transition between a confined and a deconfined phase. We also argue that some cosmological solutions could be related to the inflationary scenario.
In this paper, we analyze a proposed gravity dual to a SU(N) Bose-Hubbard model, as well as const... more In this paper, we analyze a proposed gravity dual to a SU(N) Bose-Hubbard model, as well as construct a holographic dual of a SU(N) Fermi-Hubbard model from D-branes in string theory. In both cases, the SU(N) is dynamical, i.e. the hopping degrees of freedom are strongly coupled to SU(N) gauge bosons which themselves are strongly interacting. The vacuum expectation value (VEV) of the hopping term (i.e. the hopping energy) is analyzed in the gravity dual as a function of the bulk mass of the field dual to the hopping term, as well as of the coupling constants of the model. The bulk mass controls the anomalous dimension (i.e. the critical exponent) of the hopping term in the SU(N) Bose-Hubbard model. We compare the hopping energy to the corresponding result in a numerical simulation of the ungauged SU(N ) Bose-Hubbard model. We find agreement when the hopping parameter is smaller than the other couplings. Our analysis shows that the kinetic energy increases as the bulk mass increases,...
We study SU(N) Yang-Mills-Chern-Simons theory in the presence of defects that shift the Chern-Sim... more We study SU(N) Yang-Mills-Chern-Simons theory in the presence of defects that shift the Chern-Simons level from a holographic point of view by embedding the system in string theory. The model is a D3-D7 system in Type IIB string theory, whose gravity dual is given by the AdS soliton background with probe D7-branes attaching to the AdS boundary along the defects. We holographically renormalize the free energy of the defect system with sources, from which we obtain the correlation functions for certain operators naturally associated to these defects. We find interesting phase transitions when the separation of the defects as well as the temperature are varied. We also discuss some implications for the Fractional Quantum Hall Effect and for two-dimensional QCD.
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Papers by Rene Meyer