scholarly journals Exotic $\mathbb{Z}_N$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Nathan Seiberg ◽  
Shu-Heng Shao
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Low Energy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Energy Physics ◽  
The Continuum ◽  
Continuum Field

Following our earlier analyses of nonstandard continuum quantum field theories, we study here gapped systems in 3+1 dimensions, which exhibit fractonic behavior. In particular, we present three dual field theory descriptions of the low-energy physics of the X-cube model. A key aspect of our constructions is the use of discontinuous fields in the continuum field theory. Spacetime is continuous, but the fields are not.

scholarly journals Exotic symmetries, duality, and fractons in 2+1-dimensional quantum field theory

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Nathan Seiberg ◽  
Shu-Heng Shao
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Global Symmetries ◽  
Low Energy ◽  
Field Theories ◽  
Continuum Models ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Lattice Systems ◽  
Continuum Field

We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.

scholarly journals Exotic $U(1)$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Nathan Seiberg ◽  
Shu-Heng Shao
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Global Symmetries ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Gauge Symmetries ◽  
Lattice Construction ◽  
Continuum Field

We extend our exploration of nonstandard continuum quantum field theories in 2+12+1 dimensions to 3+13+1 dimensions. These theories exhibit exotic global symmetries, a peculiar spectrum of charged states, unusual gauge symmetries, and surprising dualities. Many of the systems we study have a known lattice construction. In particular, one of them is a known gapless fracton model. The novelty here is in their continuum field theory description. In this paper, we focus on models with a global U(1)U(1) symmetry and in a followup paper we will study models with a global \mathbb{Z}_NℤN symmetry.

scholarly journals ON ALGEBRAIC STRUCTURES IMPLICIT IN TOPOLOGICAL QUANTUM FIELD THEORIES

1999 ◽  
Vol 08 (02) ◽  
pp. 125-163 ◽  
Author(s):  
Louis Crane ◽  
David Yetter
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hopf Algebra ◽  
Tensor Category ◽  
Topological Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Topological Quantum ◽  
Natural Way

We show that any 3D topological quantum field theory satisfying physically reasonable factorizability conditions has associated to it in a natural way a Hopf algebra object in a suitable tensor category. We also show that all objects in the tensor category have the structure of left-left crossed bimodules over the Hopf algebra object. For 4D factorizable topological quantum filed theories, we provide by analogous methods a construction of a Hopf algebra category.

Integrable Quantum Field Theories

2020 ◽  
pp. 575-621
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Conformal Theory ◽  
Integrable Quantum ◽  
Set Up ◽  
Integrable Quantum Field Theory

Chapter 16 covers the general properties of the integrable quantum field theories, including how an integrable quantum field theory is characterized by an infinite number of conserved charges. These theories are illustrated by means of significant examples, such as the Sine–Gordon model or the Toda field theories based on the simple roots of a Lie algebra. For the deformations of a conformal theory, it shown how to set up an efficient counting algorithm to prove the integrability of the corresponding model. The chapter focuses on two-dimensional models, and uses the term ‘two-dimensional’ to denote both a generic two-dimensional quantum field theory as well as its Euclidean version.

The Principles of Renormalisation

2021 ◽  
pp. 304-328
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Expansion ◽  
Power Counting ◽  
Field Theories ◽  
Asymptotic Freedom ◽  
Green Functions ◽  
Quantum Field Theories ◽  
Quantum Field

Loop diagrams often yield ultraviolet divergent integrals. We introduce the concept of one-particle irreducible diagrams and develop the power counting argument which makes possible the classification of quantum field theories into non-renormalisable, renormalisable and super-renormalisable. We describe some regularisation schemes with particular emphasis on dimensional regularisation. The renormalisation programme is described at one loop order for φ‎4 and QED. We argue, without presenting the detailed proof, that the programme can be extended to any finite order in the perturbation expansion for every renormalisable (or super-renormalisable) quantum field theory. We derive the equation of the renormalisation group and explain how it can be used in order to study the asymptotic behaviour of Green functions. This makes it possible to introduce the concept of asymptotic freedom.

scholarly journals EXISTENCE OF ASYMPTOTIC EXPANSIONS IN NONCOMMUTATIVE QUANTUM FIELD THEORIES

2008 ◽  
Vol 20 (08) ◽  
pp. 933-949
Author(s):  
C. A. LINHARES ◽  
A. P. C. MALBOUISSON ◽  
I. RODITI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Asymptotic Behaviors ◽  
Scalar Quantum ◽  
Feynman Amplitudes ◽  
Mellin Representation ◽  
Noncommutative Quantum

Starting from the complete Mellin representation of Feynman amplitudes for noncommutative vulcanized scalar quantum field theory, introduced in a previous publication, we generalize to this theory the study of asymptotic behaviors under scaling of arbitrary subsets of external invariants of any Feynman amplitude. This is accomplished in both convergent and renormalized amplitudes.

scholarly journals Diagrammar of physical and fake particles and spectral optical theorem

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Damiano Anselmi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Field Theories ◽  
Optical Theorem ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Virtual Particles ◽  
Major Significance ◽  
Algebraic Operations

Abstract We prove spectral optical identities in quantum field theories of physical particles (defined by the Feynman iϵ prescription) and purely virtual particles (defined by the fakeon prescription). The identities are derived by means of purely algebraic operations and hold for every (multi)threshold separately and for arbitrary frequencies. Their major significance is that they offer a deeper understanding on the problem of unitarity in quantum field theory. In particular, they apply to “skeleton” diagrams, before integrating on the space components of the loop momenta and the phase spaces. In turn, the skeleton diagrams obey a spectral optical theorem, which gives the usual optical theorem for amplitudes, once the integrals on the space components of the loop momenta and the phase spaces are restored. The fakeon prescription/projection is implemented by dropping the thresholds that involve fakeon frequencies. We give examples at one loop (bubble, triangle, box, pentagon and hexagon), two loops (triangle with “diagonal”, box with diagonal) and arbitrarily many loops. We also derive formulas for the loop integrals with fakeons and relate them to the known formulas for the loop integrals with physical particles.

scholarly journals AN APPLICATION OF NEUTRIX CALCULUS TO QUANTUM FIELD THEORY

2006 ◽  
Vol 21 (02) ◽  
pp. 297-312 ◽  
Author(s):  
Y. JACK NG ◽  
H. VAN DAM
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Effective Field Theories ◽  
Quantum Gravity ◽  
Asymptotic Series ◽  
Effective Field ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Neutrix Calculus

Neutrices are additive groups of negligible functions that do not contain any constants except 0. Their calculus was developed by van der Corput and Hadamard in connection with asymptotic series and divergent integrals. We apply neutrix calculus to quantum field theory, obtaining finite renormalizations in the loop calculations. For renormalizable quantum field theories, we recover all the usual physically observable results. One possible advantage of the neutrix framework is that effective field theories can be accommodated. Quantum gravity theories will then appear to be more manageable.

On 3-dimensional homotopy quantum field theory II: The surgery approach

2014 ◽  
Vol 25 (04) ◽  
pp. 1450027 ◽  
Author(s):  
Vladimir Turaev ◽  
Alexis Virelizier
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
3 Dimensional ◽  
Topological Quantum ◽  
Topological Quantum Field Theories

Homotopy Quantum Field Theories (HQFTs) generalize more familiar Topological Quantum Field Theories (TQFTs). In generalization of the surgery construction of 3-dimensional TQFTs from modular categories, we use surgery to derive 3-dimensional HQFTs from G-modular categories.

scholarly journals INFRARED ANALYSIS OF QUANTUM FIELD THEORIES

2007 ◽  
Vol 22 (08n09) ◽  
pp. 1727-1734 ◽  
Author(s):  
MARCO FRASCA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Asymptotic Series ◽  
Field Theories ◽  
Infrared Analysis ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Yang Mills ◽  
The Given

We show that for a λϕ4 theory having many components, the solution with all equal components in the infrared regime is stable with respect to our expansion given by a recently devised approach to analyze strongly coupled quantum field theory. The analysis is extended to a pure Yang–Mills theory showing how, in this case, the given asymptotic series exists. In this way, many components theories in the infrared regime can be mapped to a single component scalar field theory obtaining their spectrum.

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