scholarly journals Dual Superconductor Model of Confinement: Quantum-String Representation of the 4D Yang–Mills Theory on a Torus and the Correlation Length away from the London Limit

Universe ◽  
2021 ◽  
Vol 8 (1) ◽  
pp. 7
Author(s):  
Dmitry Antonov
Keyword(s):  
Partition Function ◽  
Correlation Length ◽  
Wilson Loop ◽  
Gluon Condensate ◽  
Critical Value ◽  
Low Energy ◽  
Conformal Anomaly ◽  
Energy Limit ◽  
Yang Mills ◽  
String Representation

This paper is devoted to the dual superconductor model of confinement in the 4D Yang–Mills theory. In the first part, we consider the latter theory compactified on a torus, and use the dual superconductor model in order to obtain the Polchinski–Strominger term in the string representation of a Wilson loop. For a certain realistic critical value of the product of circumferences of the compactification circles, which is expressed in terms of the gluon condensate and the vacuum correlation length, the coupling of the Polchinski–Strominger term turns out to be such that the string conformal anomaly cancels out, making the string representation fully quantum. In the second part, we use the analogy between the London limit of the dual superconductor and the low-energy limit of the 4D compact QED, to obtain the partition function of the dual superconductor model away from the London limit. There, we find a decrease of the vacuum correlation length, and derive the corresponding potential of monopole currents.

scholarly journals Fully Quantum String Representation of a Wilson Loop in the Finite-Temperature 3D Yang–Mills Theory

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 688
Author(s):  
Dmitry Antonov
Keyword(s):  
Critical Temperature ◽  
Finite Temperature ◽  
Wilson Loop ◽  
Conformal Anomaly ◽  
Yang Mills ◽  
Quantum Description ◽  
String Representation ◽  
Confinement Phase

We demonstrate the emergence of the Polchinski–Strominger term in the string representation of a Wilson loop in the confinement phase of the finite-temperature 3D Yang–Mills theory. At a temperature which is roughly twice smaller than the deconfinement critical temperature, the value of the coupling of that term becomes such that the string conformal anomaly cancels out, thereby admitting a fully quantum description of the quark–antiquark string in 3D rather than 26D.

scholarly journals ON THE CONFORMAL ANOMALY FROM HIGHER DERIVATIVE GRAVITY IN AdS/CFT CORRESPONDENCE

2000 ◽  
Vol 15 (03) ◽  
pp. 413-428 ◽  
Author(s):  
SHIN'ICHI NOJIRI ◽  
SERGEI D. ODINTSOV
Keyword(s):  
Effective Action ◽  
Einstein Gravity ◽  
Low Energy ◽  
Field Theories ◽  
Conformal Anomaly ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Yang Mills ◽  
Conformal Field ◽  
Higher Derivative

We follow Witten's proposal1 in the calculation of conformal anomaly from (d + 1)-dimensional higher derivative gravity via AdS/CFT correspondence. It is assumed that some d-dimensional conformal field theories have a description in terms of above (d + 1)-dimensional higher derivative gravity which includes not only the Einstein term and cosmological constant but also curvature squared terms. The explicit expression for two-dimensional and four-dimensional anomalies is found, it contains higher derivative corrections. In particular, it is shown that not only Einstein gravity but also theory with the Lagrangian L =aR2 + bRμνRμν + Λ (even when a=0 or b=0) is five-dimensional bulk theory for [Formula: see text] super-Yang–Mills theory in AdS/CFT correspondence. Similarly, the d + 1 = 3 theory with (or without) Einstein term may describe d = 2 scalar or spinor CFT's. That gives new versions of bulk side which may be useful in different aspects. As application of our general formalism we find next-to-leading corrections to the conformal anomaly of [Formula: see text] supersymmetric theory from d = 5 AdS higher derivative gravity (low energy string effective action).

scholarly journals Skyrme and Faddeev models in the low-energy limit of 4d Yang–Mills–Higgs theories

2019 ◽  
Vol 945 ◽  
pp. 114675
Author(s):  
Olaf Lechtenfeld ◽  
Alexander D. Popov
Keyword(s):  
Low Energy ◽  
Energy Limit ◽  
Yang Mills

scholarly journals Dual fields of massive/massless gravitons in IR/UV completions

2021 ◽  
Author(s):  
Ashkbiz Danehkar ◽  
Hassan Alshal ◽  
Thomas L. Curtright
Keyword(s):  
Dark Matter ◽  
Laser Interferometer ◽  
Low Energy ◽  
Energy Limit ◽  
Space Antenna ◽  
Yang Mills ◽  
Energy Needs ◽  
Laser Interferometer Space Antenna ◽  
Magnetic Type ◽  
Matter Fields

In the holographic picture, the Brout-Englert-Higgs (BEH) mechanism in [Formula: see text]-dimensional Yang–Mills theories is conjectured to provide a Higgs-like mechanism for gravity in [Formula: see text] dimensions, resulting in massive (or massless) gravitons in IR (or UV) completions. Accordingly, one could imagine dual (magnetic-type) fields of massive gravitons in the IR (low-energy) limit that are coupled to the curl of their own energy–momentum, as well as to the rotation of matter fields on large scales. This hypothesis, which might solve cosmological issues currently ascribed to dark matter and dark energy, needs to be examined by the future Laser Interferometer Space Antenna mission using observations of gravitational waves emitted from extragalactic sources.

scholarly journals A low-energy limit of Yang-Mills theory on de Sitter space

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Josh Cork ◽  
Emine Şeyma Kutluk ◽  
Olaf Lechtenfeld ◽  
Alexander D. Popov
Keyword(s):  
Dimensional Space ◽  
De Sitter Space ◽  
Low Energy ◽  
Finite Cylinder ◽  
De Sitter ◽  
Energy Limit ◽  
Compact Structure ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Infinite Dimensional

Abstract We consider Yang-Mills theory with a compact structure group G on four-dimensional de Sitter space dS4. Using conformal invariance, we transform the theory from dS4 to the finite cylinder $$ \mathcal{I} $$ I × S3, where $$ \mathcal{I} $$ I = (−π/2, π/2) and S3 is the round three-sphere. By considering only bundles P → $$ \mathcal{I} $$ I × S3 which are framed over the temporal boundary ∂$$ \mathcal{I} $$ I × S3, we introduce additional degrees of freedom which restrict gauge transformations to be identity on ∂$$ \mathcal{I} $$ I × S3. We study the consequences of the framing on the variation of the action, and on the Yang-Mills equations. This allows for an infinite-dimensional moduli space of Yang-Mills vacua on dS4. We show that, in the low-energy limit, when momentum along $$ \mathcal{I} $$ I is much smaller than along S3, the Yang-Mills dynamics in dS4 is approximated by geodesic motion in the infinite-dimensional space $$ \mathcal{M} $$ M vac of gauge-inequivalent Yang-Mills vacua on S3. Since $$ \mathcal{M} $$ M vac ≅ C∞(S3, G)/G is a group manifold, the dynamics is expected to be integrable.

scholarly journals The gluon condensate in an effective SU(2) Yang–Mills theory

2019 ◽  
Vol 34 (02) ◽  
pp. 1950018
Author(s):  
A. N. Efremov
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Gluon Condensate ◽  
Energy Scale ◽  
Low Energy ◽  
Effective Theory ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Mexican Hat ◽  
Text Model

We make progress towards a derivation of a low energy effective theory for SU(2) Yang–Mills theory. This low energy action is computed to 1-loop using the renormalization group technique, taking proper care of the Slavnov–Taylor identities in the Maximal Abelian Gauge. After that, we perform the Spin-Charge decomposition in a way proposed by Faddeev and Niemi. The resulting action describes a pair of nonlinear O(3) and [Formula: see text]-models interacting with a scalar field. The potential of the scalar field is a Mexican hat and the location of the minima sets the energy scale of solitonic configurations of the [Formula: see text]-model fields whose excitations correspond to glueball states.

scholarly journals ENSEMBLE OF VORTEX LOOPS IN THE ABELIAN-PROJECTED SU(3)-GLUODYNAMICS

1999 ◽  
Vol 14 (26) ◽  
pp. 1829-1839 ◽  
Author(s):  
DMITRI ANTONOV
Keyword(s):  
Partition Function ◽  
Canonical Ensemble ◽  
Grand Canonical Ensemble ◽  
Low Energy ◽  
Essential Difference ◽  
Energy Limit ◽  
Dilute Gas ◽  
Vortex Loops ◽  
Small Vortex ◽  
Grand Canonical

Grand canonical ensemble of small vortex loops emerging in the London limit of the effective Abelian-projected theory of the SU(3)-gluodynamics is investigated in the dilute gas approximation. An essential difference of this system from the SU(2)-case is the presence of two interacting gases of vortex loops. Two alternative representations for the partition function of such a grand canonical ensemble are derived, and one of them, which is a representation in terms of the integrals over vortex loops, is employed for the evaluation of the correlators of both kinds of loops in the low-energy limit.

scholarly journals TWO-LOOP EULER–HEISENBERG EFFECTIVE ACTIONS FROM CHARGED OPEN STRINGS

2006 ◽  
Vol 21 (03) ◽  
pp. 533-557 ◽  
Author(s):  
LORENZO MAGNEA ◽  
RODOLFO RUSSO ◽  
STEFANO SCIUTO
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Field Strength ◽  
Gauge Field ◽  
Riemann Surfaces ◽  
Explicit Representation ◽  
Low Energy ◽  
Energy Limit ◽  
Open Strings ◽  
Higher Genus

We present the multiloop partition function of open bosonic string theory in the presence of a constant gauge field strength, and discuss its low-energy limit. The result is written in terms of twisted determinants and differentials on higher-genus Riemann surfaces, for which we provide an explicit representation in the Schottky parametrization. In the field theory limit, we recover from the string formula the two-loop Euler–Heisenberg effective action for adjoint scalars minimally coupled to the background gauge field.

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