Chaotic dynamics in classical lattice field theories

We study a class of lattice field theories in two dimensions that includes gauge theories. We show that in these theories it is possible to implement a broader notion of local symmetry, based on semisimple Hopf algebras. A character expansion is developed for the quasitopological field theories, and partition functions are calculated with this tool. Expected values of generalized Wilson loops are defined and studied with the character expansion.

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Lattice field theories with an energy current

Nuclear Physics B ◽

10.1016/s0550-3213(99)00567-2 ◽

2000 ◽

Vol 565 (3) ◽

pp. 487-505 ◽

Cited By ~ 5

Author(s):

John Cardy ◽

Peter Suranyi

Keyword(s):

Field Theories ◽

Energy Current ◽

Lattice Field

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IR fixed points in lattice field theories

International Journal of Modern Physics A ◽

10.1142/s0217751x14450067 ◽

2014 ◽

Vol 29 (25) ◽

pp. 1445006 ◽

Cited By ~ 8

Author(s):

L. Del Debbio

Keyword(s):

Fixed Points ◽

Predictive Models ◽

Gauge Theories ◽

Quantitative Description ◽

Electroweak Symmetry Breaking ◽

Field Theories ◽

Electroweak Symmetry ◽

Lattice Field ◽

Starting Point ◽

Theoretical Foundations

The existence of strongly-interacting infrared (IR) fixed points in gauge theories can be studied using field theories defined on a lattice. Besides their academic interest, it has been argued that these theories could be used as a starting point to construct viable models of electroweak symmetry breaking (EWSB). A quantitative description of the large-distance dynamics is mandatory in order to develop predictive models for phenomenology. In these notes, we discuss the theoretical foundations of IR conformality, and present possible ways to study the problem using the lattice formulation of gauge theories. An overview of current results and methods is discussed.

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New techniques and results for worldline simulations of lattice field theories

EPJ Web of Conferences ◽

10.1051/epjconf/201817507007 ◽

2018 ◽

Vol 175 ◽

pp. 07007 ◽

Cited By ~ 3

Author(s):

Mario Giuliani ◽

Oliver Orasch ◽

Christof Gattringer

Keyword(s):

Low Temperature ◽

Model System ◽

Field Theories ◽

Scattering Parameters ◽

New Techniques ◽

Finite Density ◽

Lattice Field

We use the complex ø4 field at finite density as a model system for developing further techniques based on worldline formulations of lattice field theories. More specifically we: 1) Discuss new variants of the worm algorithm for updating the ø4 theory and related systems with site weights. 2) Explore the possibility of canonical simulations in the worldline formulation. 3) Study the connection of 2-particle condensation at low temperature to scattering parameters of the theory.

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Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

EPJ Web of Conferences ◽

10.1051/epjconf/201817511007 ◽

2018 ◽

Vol 175 ◽

pp. 11007 ◽

Cited By ~ 1

Author(s):

Christof Gattringer ◽

Daniel Göschl ◽

Carlotta Marchis

Keyword(s):

Degrees Of Freedom ◽

Chemical Potential ◽

Space Time ◽

Field Theories ◽

Gauge Fields ◽

Chiral Model ◽

Staggered Fermions ◽

Lattice Field ◽

Principal Chiral Model ◽

Matter Fields

We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.

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