Fractional quantum field theory

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Basa, Bora

Contributors dc:contributor

• Phillips, Philip
• La Nave, Gabriele
• Stone, Michael
• Noronha, Jorge L
• Gadway, Bryce

• Nonlocal Physics
• Quantum Field Theory
• Conformal Field Theory
• Topological Condensed Matter

Statement dc:rights

• Copyright 2024 Bora Basa

Language dc:language

en, eng

Handle dc:identifier

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

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F127145