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

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

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

Universal Gibbons-Hawking-York term for theories with curvature, torsion and non-metricity

Motivated by establishing holographic renormalization for gravitational theories with non-metricity and torsion, we present a new and efficient general method for calculating Gibbons-Hawking-York (GHY) terms. Our method consists of linearizing any nonlinearity in curvature, torsion or non-metricity by introducing suitable Lagrange multipliers. Moreover, we use a split formalism for differential forms, writing them in $(n-1)+1$ dimensions. The boundary terms of the action are manifest in this formalism by means of Stokes' theorem, such that the compensating GHY term for the Dirichlet problem may be read off directly. We observe that only those terms in the Lagrangian that contain curvature contribute to the GHY term. Terms polynomial solely in torsion and non-metricity do not require any GHY term compensation for the variational problem to be well-defined. We test our method by confirming existing results for Einstein-Hilbert and four-dimensional Chern-Simons modified gravity. Moreover, we obtain new results for Lovelock-Chern-Simons and metric-affine gravity. For all four examples, our new method and results contribute to a new approach towards a systematic hydrodynamic expansion for spin and hypermomentum currents within AdS/CFT.Comment: 22+9 page