scholarly journals Strongly coupled QFT dynamics via TQFT coupling

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Mithat Ünsal
Keyword(s):  
Strong Coupling ◽  
Topological Charge ◽  
Background Field ◽  
Strong Coupling Regime ◽  
Global Symmetry ◽  
Quantum Field Theories ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Mass Gap ◽  
New Perspective

Abstract We consider a class of quantum field theories and quantum mechanics, which we couple to ℤN topological QFTs, in order to classify non-perturbative effects in the original theory. The ℤN TQFT structure arises naturally from turning on a classical background field for a ℤN 0- or 1-form global symmetry. In SU(N) Yang-Mills theory coupled to ℤN TQFT, the non-perturbative expansion parameter is exp[−SI/N] = exp[−8π2/g2N] both in the semi-classical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original SU(N) theory, we must use PSU(N) bundle and lift configurations (critical points at infinity) for which there is no obstruction back to SU(N). These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on T3 × $$ {S}_L^1 $$ S L 1 can be interpreted as tunneling events in the ’t Hooft flux background in the PSU(N) bundle. The construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between the large-N and instanton analysis. We derive the mass gap at θ = 0 and gaplessness at θ = π in $$ \mathbbm{CP} $$ CP 1 model, and mass gap for arbitrary θ in $$ \mathbbm{CP} $$ CP N−1, N ≥ 3 on ℝ2.

scholarly journals Diluted mass gap in strongly coupled non-local Yang-Mills

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Marco Frasca ◽  
Anish Ghoshal
Keyword(s):  
Field Theory ◽  
Particle Physics ◽  
Mass Scale ◽  
Local Theory ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Mass Gap ◽  
Non Local ◽  
Non Locality

Abstract We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the “infinite number of derivatives” present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.

scholarly journals Phases of a strongly coupled four-fermion theory

2018 ◽  
Vol 175 ◽  
pp. 03004 ◽  
Author(s):  
David Schaich ◽  
Simon Catterall
Keyword(s):  
Strong Coupling ◽  
Weak Coupling ◽  
Strongly Coupled ◽  
Coupling Phase ◽  
Long Range Correlations ◽  
Mass Gap ◽  
Narrow Region ◽  
Lattice Field ◽  
Lattice Symmetry ◽  
Lattice Fermion

We present ongoing investigations of a four-dimensional lattice field theory with four massless reduced staggered fermions coupled through an SU(4)-invariant fourfermion interaction. As in previous studies of four-fermion and Higgs–Yukawa models with different lattice fermion discretizations, we observe a strong-coupling phase in which the system develops a mass gap without breaking any lattice symmetry. This symmetric strong-coupling phase is separated from the symmetric weak-coupling phase by a narrow region of four-fermi coupling in which the system exhibits long-range correlations.

scholarly journals QCD, with strings attached

2016 ◽  
Vol 25 (10) ◽  
pp. 1630006 ◽  
Author(s):  
Alberto Güijosa
Keyword(s):  
String Theory ◽  
Quantum Chromodynamics ◽  
Large Class ◽  
Strong Coupling ◽  
Field Theories ◽  
Strong Coupling Regime ◽  
Efficient Tool ◽  
Strongly Coupled ◽  
Coupled Field ◽  
Gauge Gravity

In the nearly 20 years that have elapsed since its discovery, the gauge-gravity correspondence has become established as an efficient tool to explore the physics of a large class of strongly-coupled field theories. A brief overview is given here of its formulation and a few of its applications, emphasizing attempts to emulate aspects of the strong-coupling regime of quantum chromodynamics (QCD). To the extent possible, the presentation is self-contained, and does not presuppose knowledge of string theory.

scholarly journals Small instantons in weakly-gauged holographic models

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Tony Gherghetta ◽  
Alex Pomarol
Keyword(s):  
Topological Charge ◽  
Conformal Transformation ◽  
Analytic Solutions ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Interesting Class ◽  
Gauge Couplings ◽  
Topological Charges

Abstract Small instantons can play an important role in Yang-Mills theories whose gauge couplings are sizeable at small distances. An interesting class of theories where this could occur is in weakly-gauged holographic models (dual to Yang-Mills theories interacting with strongly-coupled CFTs), since gauge couplings are indeed enhanced towards the UV boundary of the 5D AdS space. However, contrary to expectations, we show that small instantons in these non-asymptotically-free models are highly suppressed and ineffective. This is due to the conservation of topological charge that forbids instantons to be localized near the UV boundary. Despite this fact we find non-trivial UV localized instanton-anti-instanton solutions of the Yang-Mills equations where the topological charges annihilate in the AdS bulk. These analytic solutions arise from a 5D conformal transformation of the uplifted 4D instanton. Our analysis therefore reveals unexpected nonperturbative configurations of Yang-Mills theories when they interact with strongly-coupled CFTs.

No Mass Gap Phase Transition in Novel Massless Dirac Fermion Material

2021 ◽  
Vol 1 ◽  
Keyword(s):  
Phase Transition ◽  
Strong Coupling ◽  
Quantum Phase Transition ◽  
Dirac Fermion ◽  
Strong Coupling Regime ◽  
Dirac Fermions ◽  
Fermion System ◽  
Mass Gap ◽  
Gap Phase ◽  
Massless Dirac Fermion

Using an organic massless Dirac fermion system, we found that massless Dirac fermions undergo a quantum phase transition without creating any mass gap even in the strong coupling regime.

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.

scholarly journals 2-Group global symmetries and anomalies in six-dimensional quantum field theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Clay Córdova ◽  
Thomas T. Dumitrescu ◽  
Kenneth Intriligator
Keyword(s):  
Global Symmetries ◽  
Group Symmetry ◽  
Field Theories ◽  
Global Symmetry ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Six Dimensions ◽  
String Theories

Abstract We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength f(2), naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current J(2)∼ ∗Tr (f(2) ∧ f(2)). We show that suitable mixed anomalies involving the gauge field f(2) and ordinary 0-form global symmetries, such as flavor or Poincaré symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tensors to fuse into the 2-form current J(2). We discuss several features of 2-group symmetry in six dimensions, many of which parallel the four-dimensional case. The majority of six-dimensional supersymmetric conformal field theories (SCFTs) and little string theories have infrared phases with non-abelian gauge fields. We show that the mixed anomalies leading to 2-group symmetries can be present in little string theories, but that they are necessarily absent in SCFTs. This allows us to establish a previously conjectured algorithm for computing the ’t Hooft anomalies of most SCFTs from the spectrum of weakly-coupled massless particles on the tensor branch of these theories. We then apply this understanding to prove that the a-type Weyl anomaly of all SCFTs with a tensor branch must be positive, a > 0.

A solvable four-dimensional model with gauge symmetry

1992 ◽  
Vol 70 (6) ◽  
pp. 441-450 ◽  
Author(s):  
D. G. C. McKeon ◽  
T. N. Sherry
Keyword(s):  
Vector Field ◽  
Lagrange Multiplier ◽  
Path Integral ◽  
Equations Of Motion ◽  
Background Field ◽  
Dynamical Theory ◽  
Vector Model ◽  
Quantum Field Theories ◽  
Yang Mills ◽  
Classical Lagrangian

Recently, interest has been focused on quantum field theories in which a Lagrange multiplier field occurs in the classical Lagrangian. This has the effect of restricting the sum over classical paths in the path integral to solutions of the classical field equation. Examples of such theories are the dynamical theory of two-dimensional gravity proposed by Jackiw and Teitelboim, the Chern–Simons formulation of gravity in 2 + 1 dimensions by Witten, and the path-integral formulation of classical systems by Gozzi. We examine, in this paper, a gauge theory in which a vector field [Formula: see text] acts as a Lagrange multiplier in the classical Lagrangian, ensuring that a vector field [Formula: see text] satisfies the Yang–Mills equations of motion. Quantization can be carried out either using BRST quantization or by using the Faddeev–Popov procedure. Either by explicitly integrating over the field [Formula: see text] and its associated ghost fields, or by directly examining the Feynman perturbation theory, it can be established that all diagrams beyond one-loop order vanish, allowing one to compute the one-particle irreducible generating functional exactly. Background-field quantization is introduced to simplify the renormalization program. The β function is computed in closed form. In an appendix we show how our interaction can be derived from Yang–Mills theory based on a group G or by considering the Yang–Mills theory for a group IG. This can be extended to deal with four interacting gauge fields. A second appendix deals with a scalar model that superficially resembles our vector model.

scholarly journals Topological terms and anomaly matching in effective field theories on ℝ3 × 𝕊1. Part I. Abelian symmetries and intermediate scales

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Erich Poppitz ◽  
F. David Wandler
Keyword(s):  
Effective Field Theories ◽  
Gauge Theories ◽  
Background Field ◽  
Effective Field ◽  
Field Theories ◽  
Global Symmetry ◽  
Dirac Fermions ◽  
Yang Mills ◽  
Local Background ◽  
Weyl Fermion

Abstract We explicitly calculate the topological terms that arise in IR effective field theories for SU(N) gauge theories on ℝ3 × 𝕊1 by integrating out all but the lightest modes. We then show how these terms match all global-symmetry ’t Hooft anomalies of the UV description. We limit our discussion to theories with abelian 0-form symmetries, namely those with one flavour of adjoint Weyl fermion and one or zero flavours of Dirac fermions. While anomaly matching holds as required, it takes a different form than previously thought. For example, cubic- and mixed-U(1) anomalies are matched by local background-field-dependent topological terms (background TQFTs) instead of chirallagrangian Wess-Zumino terms. We also describe the coupling of 0-form and 1-form symmetry backgrounds in the magnetic dual of super-Yang-Mills theory in a novel way, valid throughout the RG flow and consistent with the monopole-instanton ’t Hooft vertices. We use it to discuss the matching of the mixed chiral-center anomaly in the magnetic dual.

scholarly journals The lattice and quantized Yang–Mills theory

2015 ◽  
Vol 30 (36) ◽  
pp. 1530027
Author(s):  
Michael Creutz
Keyword(s):  
Strong Coupling ◽  
First Principles ◽  
Nuclear Force ◽  
Perturbative Expansion ◽  
Strong Interactions ◽  
Strong Coupling Regime ◽  
Quark Confinement ◽  
Yang Mills ◽  
Low Energies

Quantized Yang–Mills fields lie at the heart of our understanding of the strong nuclear force. To understand the theory at low energies, we must work in the strong coupling regime. The primary technique for this is the lattice. While basically an ultraviolet regulator, the lattice avoids the use of a perturbative expansion. I discuss the historical circumstances that drove us to this approach, which has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles.

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