Developments in non-relativistic field theory and complexity

Abstract

This thesis focuses on two research areas: non-relativistic field theories and complexity. In the first part we review the general classification of the trace anomaly for 2+1 dimensional field theories coupled to a Newton-Cartan background and we apply the heat kernel method to compute the trace anomaly for specific theories. We find a relation with the conformal anomaly of the 3+1 dimensional relativistic counterpart which suggests the existence of a non-relativistic version of the a-theorem. We consider a model realizing a $\mathcal{N}=2$ supersymmetric extension of the Bargmann group in 2+1 dimensions with non-vanishing superpotential, obtained by null reduction of a relativistic Wess-Zumino model. We check that the superpotential is protected against quantum corrections as in the relativistic parent theory, thus finding a non-relativistic version of the non-renormalization theorem. We find evidence that the theory is one-loop exact, due to the causal structure of the non-relativistic propagator together with mass conservation. In the second part of the thesis we review the holographic conjectures proposed by Susskind to describe the time-evolution of the Einstein-Rosen bridge in gravity: the complexity=volume and complexity=action. We investigate both the volume and the action for black holes living in warped ${\mathrm{AdS}}_3$ spacetime. There exist extensions of the proposals when the dual state from the field theory side is mixed; we then analytically compute the subregion action complexity for a general segment on the boundary in the BTZ black hole background, finding that it is equal to the sum of a linearly divergent term proportional to the size of the subregion and of a term proportional to the entanglement entropy. We also find that mutual holographic complexity carries a different content compared to mutual information. This means that entropy is not enough!

arXiv comment226 pages with several figures; PhD thesis; mostly based on arXiv:1705.02229, arXiv:1711.00910, arXiv:1804.07521, arXiv:1806.06216, arXiv:1904.08404, arXiv:1906.09345, arXiv:1910.00526 ; additional comments and details are added; V2: reference added

References in corpus (105)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The Black Hole in Three Dimensional Space Time
• Black Hole Entropy is Noether Charge
• A Supersymmetry Primer
• Geometry of the 2+1 Black Hole
• Eternal Black Holes in AdS
• Universality in Few-body Systems with Large Scattering Length
• Complexity Equals Action
• On Renormalization Group Flows in Four Dimensions
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Complexity and Shock Wave Geometries
• Time Evolution of Entanglement Entropy from Black Hole Interiors
• Complexity, action, and black holes
• Renormalization of the Three-Body System with Short-Range Interactions
• The Gravity Dual of a Density Matrix
• Causality & holographic entanglement entropy
• Towards Complexity for Quantum Field Theory States
• Warped AdS_3 Black Holes
• The Three-Boson System with Short-Range Interactions
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Nonrelativistic conformal field theories
• Gravitational action with null boundaries
• Hall Viscosity and Electromagnetic Response
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• Comments on Holographic Complexity
• State-Dependent Bulk-Boundary Maps and Black Hole Complementarity
• Complexity of Formation in Holography
• Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
• Torsional Newton-Cartan Geometry and Lifshitz Holography
• Circuit Complexity in Fermionic Field Theory
• Complexity Growth for AdS Black Holes
• Warped Conformal Field Theory
• Causal Holographic Information
• Spacetime Symmetries of the Quantum Hall Effect
• Emergent Supersymmetry from Strongly Interacting Majorana Zero Modes
• Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals
• Emergence of supersymmetry at a critical point of a lattice model
• Lifshitz Space-Times for Schroedinger Holography
• Comments on the Necessity and Implications of State-Dependence in the Black Hole Interior
• Higher Spin Black Holes from CFT
• Chiral Scale and Conformal Invariance in 2D Quantum Field Theory
• Schroedinger Invariance from Lifshitz Isometries in Holography and Field Theory
• On the coupling of Galilean-invariant field theories to curved spacetime
• Subsystem Complexity and Holography
• Path-Integral Complexity for Perturbed CFTs
• Warped Conformal Field Theory as Lower Spin Gravity
• Universal properties and the first law of black hole inner mechanics
• Newton-Cartan Geometry and the Quantum Hall Effect
• Complexity of Mixed States in QFT and Holography
• Aharonov-Bohm Scattering, Contact Interactions and Scale Invariance
• On Complexity for Higher Derivative Gravities
• Revisiting non-relativistic limits
• Entanglement Entropy in Warped Conformal Field Theories
• Holographic Subregion Complexity from Kinematic Space
• Extended Superconformal Galilean Symmetry in Chern-Simons Matter Systems
• Holographic Complexity And Cosmological Singularities
• Simulating Wess-Zumino Supersymmetry Model in Optical Lattices
• Three dimensional origin of Godel spacetimes and black holes
• Modifications to Holographic Entanglement Entropy in Warped CFT
• Holographic Complexity for Defects Distinguishes Action from Volume
• Subregion Action and Complexity
• Conserved charges and thermodynamics of the spinning Godel black hole
• Complexity growth rates for AdS black holes in massive gravity and $f(R)$ gravity
• Complexity change under conformal transformations in AdS${}_3$/CFT${}_2$
• Surface Counterterms and Regularized Holographic Complexity
• Nonrelativistic Superconformal M2-Brane Theory
• Hopfing and Puffing Warped Anti-de Sitter Space
• Divergences in the rate of complexification
• 3D supergravity from wrapped M5-branes
• A Non-Relativistic Weyl Anomaly
• Stringy Schroedinger truncations
• On complexity growth in massive gravity theories, the effects of chirality and more
• WdW-patches in AdS${}_3$ and complexity change under conformal transformations II
• Locality and anomalies in warped conformal field theory
• Emergent supersymmetry at the Ising-Berezinskii-Kosterlitz-Thouless multicritical point
• Generalized Gravitational Entropy for Warped Anti-de Sitter Space
• Warped black holes in 3D general massive gravity
• Entanglement Entropy in Non-Relativistic Field Theories
• Holographic Subregion Complexity for Singular Surfaces
• Supersymmetric Gödel and warped black holes in string theory
• Anomalies for Galilean fields
• On Complexity Growth in Minimal Massive 3D Gravity
• Holographic Purification Complexity
• Scaling and conformal symmetries for plane gravitational waves
• From accelerating and Poincaré coordinates to black holes in spacelike warped AdS${}_3$, and back
• Warped Black Holes in Lower-Spin Gravity
• A Note on Subregion Holographic Complexity
• Entanglement Entropy and Subregion Complexity in Thermal Perturbations around Pure-AdS Spacetime
• Thermodynamic Information Geometry and Complexity Growth of Warped AdS Black Hole and the WAdS${}_3$/CFT${}_2$ Correspondence
• On subregion holographic complexity and renormalization group flows
• Super-Galilei Invariant Field Theories in 2+1 Dimensions
• On the Heat Kernel and Weyl Anomaly of Schrödinger invariant theory
• Lectures on entanglement entropy in field theory and holography
• On Supersymmetric Lifshitz Field Theories
• Renormalization properties of a Galilean Wess-Zumino model
• Finite-Scale Emergence of 2+1D Supersymmetry at First-Order Quantum Phase Transition
• On-shell actions with lightlike boundary data
• Warped-AdS3 black holes with scalar halo
• Spinor fields in general Newton-Cartan backgrounds
• Holomorphic Structure and Quantum Critical Points in Supersymmetric Lifshitz Field Theories
• Gravitational anomalies on the Newton-Cartan background
• Nonrelativistic trace and diffeomorphism anomalies in particle number background
• Effective field theory for one-dimensional nonrelativistic particles with contact interaction
• Bosonization in Non-Relativistic CFTs