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!

226 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 (27)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Complexity and Shock Wave Geometries
• Causality & holographic entanglement entropy
• Warped AdS_3 Black Holes
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Nonrelativistic conformal field theories
• Gravitational action with null boundaries
• Spacetime Symmetries of the Quantum Hall Effect
• 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
• Warped Conformal Field Theory as Lower Spin Gravity
• Revisiting non-relativistic limits
• Simulating Wess-Zumino Supersymmetry Model in Optical Lattices
• Nonrelativistic Superconformal M2-Brane Theory
• WdW-patches in AdS${}_3$ and complexity change under conformal transformations II
• On complexity growth in massive gravity theories, the effects of chirality and more
• Emergent supersymmetry at the Ising-Berezinskii-Kosterlitz-Thouless multicritical point
• Warped black holes in 3D general massive gravity
• Supersymmetric Gödel and warped black holes in string theory
• On Complexity Growth in Minimal Massive 3D Gravity
• From accelerating and Poincaré coordinates to black holes in spacelike warped AdS${}_3$, and back
• Thermodynamic Information Geometry and Complexity Growth of Warped AdS Black Hole and the WAdS${}_3$/CFT${}_2$ Correspondence
• Lectures on entanglement entropy in field theory and holography
• Renormalization properties of a Galilean Wess-Zumino model
• Bosonization in Non-Relativistic CFTs