Symmetry Breaking in Melonic Models

Abstract

This thesis discusses novel symmetry breaking phenomena observed in models with a melonic large N limit, such as Sachdev-Ye-Kitaev(SYK) models and tensor models. In such a limit, these models are often nearly conformal. However, this thesis provides examples where the would-be nearly conformal points violate unitarity and are, therefore, not realized as the physical solutions of the models. In those cases, the physical solutions may spontaneously break certain symmetries. Chapter 2 is based on work with Jaewon Kim, Igor R. Klebanov and Grigory Tarnopolsky. It is devoted to the study of a system consisting of two Majorana tensor models coupled through a quartic tetrahedral interaction. It shows that, for certain range of the coupling, the nearly conformal solution becomes non-unitary and unstable. It identifies the operator whose scaling dimension goes complex, and shows through numerical methods that at low temperature, such an operator acquires a vacuum expectation value(VEV), which spontaneously breaks a Z2 particle hole symmetry. Chapter 3 is based on work with Igor R. Klebanov, Alexey Milekhin, and Grigory Tarnopolsky. It extends the work of chapter 2 to the spontaneous breaking of a U(1) symmetry. In particular, Goldstone modes are identified. Specifically, the chapter contains the study of a system consisting of two copies of the complex Sachdev-Ye-Kitaev (SYK) or tensor models coupled by a quartic term preserving the U(1) x U(1) symmetry. It reveals that the scaling dimension of certain bilinear operator charged under axial U(1) becomes complex for some range of the quartic coupling, and at low temperature such an operator condenses, thus spontaneously breaks U(1) symmetry. Chapter 4 is based on work with Matthew Heydeman and Gustavo Joaquin Turiaci. It is devoted to the study of N=2 supersymmetric SYK models with complex fermions, at non-zero charge. A new N=2 SYK model with multiple U(1) symmetries is also proposed. In both models, a nearly conformal solution emerges at low temperatures. For a critical charge a high entropy to low entropy phase transition is found through numerical methods. In the new model proposed, such a low entropy phase spontaneously breaks the N=2 supersymmetry.