Symmetry-Resolved Entanglement in AdS3{}_3/CFT2{}_2 coupled to U(1)U(1) Chern-Simons Theory

We consider symmetry-resolved entanglement entropy in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS${}_3$, namely the Ryu-Takayanagi geodesic minimally coupled to the $U(1)$ Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged $U(1)$ vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the $U(1)$ Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincar\'e patch and global AdS${}_3$, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level $k$, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $\hat{\mathfrak{u}}{(1)_k}$ Kac-Moody type. Employing the $\hat{\mathfrak{u}}{(1)_k}$ Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.Comment: 28 pages plus appendices, 3 Figure

Towards hydrodynamics without an entropy current

We present a generating functional which describes the equilibrium thermodynamic response of a relativistic system to external sources. A variational principle gives rise to constraints on the response parameters of relativistic hydrodynamics without making use of an entropy current. Our method reproduces and extends results available in the literature. It also provides a technique for efficiently computing n-point zero-frequency hydrodynamic correlation functions without the need to solve the equations of hydrodynamics.Comment: 4+epsilon pages, v2: comments and references adde

Spacetime Emergence in the Robertson-Walker Universe from a Matrix model

Using a novel, string theory-inspired formalism based on a Hamiltonian constraint, we obtain a conformal mechanical system for the spatially flat four-dimensional Robertson-Walker Universe. Depending on parameter choices, this system describes either a relativistic particle in the Robertson-Walker background, or metric fluctuations of the Robertson-Walker geometry. Moreover we derive a tree-level M-theory matrix model in this time-dependent background. Imposing the Hamiltonian constraint forces the spacetime geometry to be fuzzy near the big bang, while the classical Robertson-Walker geometry emerges as the Universe expands. From our approach we also derive the temperature of the Universe interpolating between the radiation and matter dominated eras.Comment: 4 pages - accepted for publication in Physical Review Letter

Holographic (De)confinement Transitions in Cosmological Backgrounds

For type IIB supergravity with a running axio-dilaton, we construct bulk solutions which admit a cosmological background metric of Friedmann-Robertson-Walker type. These solutions include both a dark radiation term in the bulk as well as a four-dimensional (boundary) cosmological constant, while gravity at the boundary remains non-dynamical. We holographically calculate the stress-energy tensor, showing that it consists of two contributions: The first one, generated by the dark radiation term, leads to the thermal fluid of N = 4 SYM theory, while the second, the conformal anomaly, originates from the boundary cosmological constant. Conservation of the boundary stress tensor implies that the boundary cosmological constant is time-independent, such that there is no exchange between the two stress-tensor contributions. We then study (de)confinement by evaluating the Wilson loop in these backgrounds. While the dark radiation term favours deconfinement, a negative cosmological constant drives the system into a confined phase. When both contributions are present, we find an oscillating universe with negative cosmological constant which undergoes periodic (de)confinement transitions as the scale of three space expands and re-contracts.Comment: 31 pages, 5 figures, v2: Reference adde

Holography in External Fields and in Time Dependent Backgrounds

Holographic models, i.e. theories describing higher-dimensional gravitational physics in terms of lower-dimensional models without gravitation and vice versa, come in two guises in string theory: The AdS/CFT-Correspondence reformulates strongly coupled nonabelian field theories in terms of weakly coupled gravity theories on Anti-de Sitter space-times, thus allowing studies of strongly coupled gauge theory dynamics. On the other hand, eleven-dimensional quantum gravity (M-theory) can be reformulated in terms of matrix models, field theories of matrix-valued degrees of freedom in 0+1 dimensions. This thesis is concerned with both aspects of holography in string theory: In chapter 3, a way of holographically introducing constant electric and magnetic background fields in the D3-D7 model of holographic quarks is laid out. Magnetic background fields are found to induce spontaneous chiral symmetry breaking, while electric fields induce a vacuum instability which can be interpreted in terms of Schwinger pair production of quark-antiquark pairs. Chapter 4 of this thesis is concerned with the introduction of holographic Fayet-Iliopoulos terms in the D3-D7 model, which lead to spontaneous breaking of supersymmetry and gauge symmetry. The holographic dual of the N=2 Fayet-Iliopoulos term, a particular mode of the Kalb-Ramond field, is identified. Chapter 5 of this thesis is concerned with matrix models in the Friedmann-Robertson-Walker universe: A bosonic matrix model in this particular background is derived for a general scale factor, and the emergence of space-time away from cosmological singularities is shown by a semiclassical argument. An in-depth introduction into string theory, holography, and the AdS/CFT correspondence can be found in chapter 2, while chapter 1 and 6 respectively contain a general introduction and a discussion of the results of this thesis

Effective Hopping in Holographic Bose and Fermi-Hubbard Models

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, due to increased contributions from the IR. The holographic Bose-Hubbard model is then compared with the string theory construction of a SU(N) Fermi-Hubbard model. The string theory construction makes it possible to describe fluctuations around a half-filled state in the supergravity limit, which map to O(1) occupation number fluctuations in the Fermi-Hubbard model at half filling. Finally, the VEV of the Bose-Hubbard model is shown to agree with the one of the fermionic Hubbard model with the help of a two-site version of the Jordan-Wigner transformation

Disorder in AdS3_3/CFT2_2

We perturbatively study marginally relevant quenched disorder in AdS$_3$/CFT$_2$ to second order in the disorder strength. Using the Chern-Simons formulation of AdS$_3$ gravity for the Poincar\'e patch, we introduce disorder via the chemical potentials. We discuss the bulk and boundary properties resulting from the disorder averaged metric. The disorder generates a small mass and angular momentum. In the bulk and the boundary, we find unphysical features due to the disorder average. Motivated by these features, we propose a Poincar\'e-Lindstedt-inspired resummation method. We discuss how this method enables us to remove all of the unphysical features.Comment: 21 pages, v2: citations adde