Fractional quantum field theory

Basa, Bora

Permalink

https://hdl.handle.net/2142/127145 Copy

Description

Title

Fractional quantum field theory

Author(s)

Basa, Bora

Issue Date

2024-08-29

Director of Research (if dissertation) or Advisor (if thesis)

• Phillips, Philip
• La Nave, Gabriele

Doctoral Committee Chair(s)

Stone, Michael

Committee Member(s)

• Noronha, Jorge L
• Gadway, Bryce

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• nonlocal physics
• quantum field theory
• conformal field theory
• topological condensed matter

Abstract

We consider field theoretic models constructed out of pseudo-differential operators, with an emphasis on the Laplacian raised to a real power. In recent years, such models have received a great deal of attention across energy scales and flavors, especially in cases where they serve as nonlocal duals to local models. Borrowing from geometric analysis, we develop this correspondence using the machinery of so-called metric measure spaces. We find that the nature of nonlocality induced by such operators is not always robust to quantization: path integral-quantized massless fields that classically solve $(-\Delta)^s\phi=0$ retain an area law scaling of their entanglement entropy. Extensive scaling obtains under arbitrarily small local deformations. We expand on this interplay between locality and quantization in the 2-dimensional conformal setting by formally constructing CFTs that realize a fractional analogue of the Virasoro algebra. This generalized algebra has the feature that its central charge is not only not a c-number but a state-dependent operator. This is further conceptualized as a grading of the space of flows around a fractional Gaussian fixed point. We consider also elements of fractional quantum field theory outside its implications for locality. In particular, we provide lattice toy model of the projective Dirac operator, which, as a field theory, can be defined independently of spin structure and has rational $\hat A$-genus. This model, which is an algebraic extension of the Kitaev chain Hamiltonian, possesses a rational winding number like its conjectural field theoretic partner. We demonstrate that this regime is robust against disorder and (psudeo)metallic in nature.

Graduation Semester

2024-12

Type of Resource

Thesis

Handle URL

https://hdl.handle.net/2142/127145

Copyright and License Information

Copyright 2024 Bora Basa

Owning Collections