Constructing SU(N) fractional instantons

Abstract

We study self-dual SU(N) gauge field configurations on the 4 torus with twisted boundary conditions, known as fractional instantons. Focusing on the minimum non-zero action case, we generalize the constant field strength solutions discovered by `t Hooft and valid for certain geometries. For the general case, we construct the vector potential and field strength in a power series expansion in a deformation parameter of the metric. The next to leading term is explicitly computed. The methodology is an extension of that used by the author for SU(2) fractional instantons and for vortices in two-dimensional Abelian Higgs models. Obviously, these solutions can also be seen as self-dual configurations in ${\mathbb{R}}^4$ having a crystal structure, where each node of the crystal carries a topological charge of $1/N$.

arXiv commentpdflatex. 29 pages, no figures

References in corpus (26)

• Periodic Instantons with non-trivial Holonomy
• SU(2) Calorons and Magnetic Monopoles
• Exact T-duality between Calorons and Taub-NUT spaces
• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• Instantons and Magnetic Monopoles on $R^3\times S^1$ with Arbitrary Simple Gauge Groups
• Self-dual vortex-like configurations in SU(2) Yang-Mills Theory
• Investigating Yang-Mills theory and Confinement as a function of the spatial volume
• Calorons on the lattice - a new perspective
• Study of SU(3) vortex-like configurations with a new maximal center gauge fixing method
• Gauge invariant structures and Confinement
• Numerical study of Yang-Mills classical solutions on the twisted torus
• Do classical configurations produce Confinement?
• Instanton-like Contributions to the Dynamics of Yang-Mills Fields on the Twisted Torus
• Vortex configurations in the large N limit
• Perturbative construction of self-dual configurations on the torus
• Expansion for the solutions of the Bogomolny equations on the torus
• Nahm dualities on the torus - a synthesis
• On Nahm's transformation with twisted boundary conditions
• Tachyonic instabilities in 2+1 dimensional Yang-Mills theory and its connection to Number Theory
• From Perturbation Theory to Confinement: How the String Tension is built up
• Numerical analysis of fractional charge solutions on the torus
• Yang-Mills classical solutions and fermionic zero modes from lattice calculations
• Once more on $\theta$-vacua in $2+1$ dimensional QED and 3+1 dimensional gluodynamics
• Dynamics of critical vortices on the torus and on the plane
• Quantum corrections to vortex masses and energies

Cited by in corpus (14)

• Nonperturbative effects in the Standard Model with gauged 1-form symmetry
• The gaugino condensate from asymmetric four-torus with twists
• Towards a semi-classical description of QCD vacuum around $T_c$
• Gauge theory geography: charting a path between semiclassical islands
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• Strongly coupled QFT dynamics via TQFT coupling
• TQFT at work for IR-renormalons, resurgence and Lefschetz decomposition
• Cluster expansion and resurgence in Polyakov model
• Numerical evidence for fractional topological objects in SU(3) gauge theory
• Comparison of smoothening flows for the topological charge in QCD-like theories
• Correlating confinement to topological fluctuations near the crossover transition in QCD
• The mixed $0$-form/$1$-form anomaly in Hilbert space: pouring new wine into old bottles
• Analytic Approach for Computation of Topological Number of Integrable Vortex on Torus
• Polyakov Model in 't Hooft flux background: A quantum mechanical reduction with memory