We examine a double trace deformation of SU(N) Yang-Mills theory which, for large $N$ and large volume, is equivalent to unmodified Yang-Mills theory up to $O(1/N^2)$ corrections. In contrast to the unmodified theory, large $N$ volume independence is valid in the deformed theory down to arbitrarily small volumes. The double trace deformation prevents the spontaneous breaking of center symmetry which would otherwise disrupt large $N$ volume independence in small volumes. For small values of $N$, if the theory is formulated on $\R^3 \times S^1$ with a sufficiently small compactification size $L$, then an analytic treatment of the non-perturbative dynamics of the deformed theory is possible. In this regime, we show that the deformed Yang-Mills theory has a mass gap and exhibits linear confinement. Increasing the circumference $L$ or number of colors $N$ decreases the separation of scales on which the analytic treatment relies. However, there are no order parameters which distinguish the small and large radius regimes. Consequently, for small $N$ the deformed theory provides a novel example of a locally four-dimensional pure gauge theory in which one has analytic control over confinement, while for large $N$ it provides a simple fully reduced model for Yang-Mills theory. The construction is easily generalized to QCD and other QCD-like theories.
We review some recent results related to the notion of volume independence in SU(N) Yang-Mills theories. The topic is discussed in the context of gauge theories living on a d-dimensional torus with twisted boundary conditions. After a brief introduction reviewing the formalism for introducing gauge fields on a torus, we discuss how volume independence arises in perturbation theory. We show how, for appropriately chosen twist tensors, perturbative results to all orders in the 't Hooft coupling depend on a specific combination of the rank of the gauge group (N) and the periods of the torus (l) g…
We simulate four-dimensional center-stabilized lattice Yang-Mills theories on R^3 x S^1 with a newly developed pseudo-heatbath algorithm. We analyze the phase structure of such theories, namely the bulk transition and the spontaneous breaking of the center symmetry associated with the compact direction.
We derive a generalized Nielsen identity for the case of Yang-Mills theories that include some classical fields. We discuss under which circumstances the effective action of the classical fields (i.e., after integration of quantum fields) becomes gauge fixing independent. We conclude that classical test fields provide a physical insight into the problem of the gauge-fixing dependence of the quantum effective action.
We calculate the rate of the decay of a metastable vacuum state in $SU(N)$ gauge theory on ${\mathbb R}^3 \times {\mathbb S}^1$ space with a double trace deformation suggested by Ünsal and Yaffe. The derived analytical expression for the exponential factor in the decay rate, including the dependence on the parameter $θ$, gives the exact behavior in the leading power of $N$ in the limit of large $N$ and provides a better approximation than a recently found in the literature numerical result.
Volume independence in large $\Nc$ gauge theories may be viewed as a generalized orbifold equivalence. The reduction to zero volume (or Eguchi-Kawai reduction) is a special case of this equivalence. So is temperature independence in confining phases. In pure Yang-Mills theory, the failure of volume independence for sufficiently small volumes (at weak coupling) due to spontaneous breaking of center symmetry, together with its validity above a critical size, nicely illustrate the symmetry realization conditions which are both necessary and sufficient for large $\Nc$ orbifold equivalence. The exi…
We study the Eguchi-Kawai reduction in the strong-coupling domain of gauge theories via the gravity dual of N=4 super-Yang-Mills on R^3xS^1. We show that D-branes geometrize volume independence in the center-symmetric vacuum and give supergravity predictions for the range of validity of reduced large-N models at strong coupling.
In this work we investigate the effects of the Gribov prescription to get rid of zero-modes of the Faddeev-Popov operator, at one-loop order in perturbation theory, in the Landau-DeWitt gauge. Quantum fluctuations are taken around a transverse background gauge field. The one-loop effective action is explicitly computed, and the behavior of the gauge and ghost fields propagators are carefully investigated. At one-loop and for generic transverse background configurations the effective action is found to be \textit{not} background invariant, as expected, due to a non-vanishing background contribu…
The gauge dependence of the time-ordered products for Yang-Mills theories is analysed in perturbation theory by means of the causal method of Epstein and Glaser together with perturbative gauge invariance. This approach allows a simple inductive proof of the gauge independence of the physical S-matrix.
We study aspects of the large-N volume independence on R**3 x L**G, where L**G is a G-site lattice for Yang-Mills theory with adjoint Wilson-fermions. We find the critical number of lattice sites above which the center-symmetry analysis on L**G agrees with the one on the continuum S**1. For Wilson parameter set to one and G>=2, the two analyses agree. One-loop radiative corrections to Wilson-line masses are finite, reminiscent of the UV-insensitivity of the Higgs mass in deconstruction/Little-Higgs theories. Even for theories with G=1, volume independence in QCD(adj) may be guaranteed to work …
Background independence of noncommutative Yang-Mills theory on $\mathbb R^n$ is discussed. The quantity $θ\hat F θ- θ$ is found to be background dependent at subleading order, and it becomes background independent only when the ordinary gauge field strength $F$ is constant. It is shown that, at small values of $B$, the noncommutative Dirac-Born-Infeld action possesses $Λ$-symmetry at least to subleading order in $θ$ if $F$ damps fast enough at infinity.
A path integral description of an effective action of monopoles in Abelian projections of Yang-Mills theories is discussed and used to establish a projection independence of the effective action. A dynamic regime in which the effective dynamics may contain massive solitonic excitations is described.
We investigate dynamics of the homogeneous time-dependent SU(2) Yang-Mills fields governed by the non-Abelian Born-Infeld lagrangian which arises in superstring theory as a result of summation of all orders in the string slope parameter $α'$. It is shown that generically the Born-Infeld dynamics is less chaotic than that in the ordinary Yang-Mills theory, and at high enough field strength the Yang-Mills chaos is stabilized. More generally, a smothering effect of the string non-locality on behavior of classical fields is conjectured.
In this paper, we consider two-dimensional N=(4,4) supersymmetric Yang-Mills (SYM) theory and deform it by a mass parameter M with keeping all supercharges. We further add another mass parameter m in a manner to respect two of the eight supercharges and put the deformed theory on a two-dimensional square lattice, on which the two supercharges are exactly preserved. The flat directions of scalar fields are stabilized due to the mass deformations, which gives discrete minima representing fuzzy spheres. We show in the perturbation theory that the lattice continuum limit can be taken without any f…
We construct a lattice formulation of a mass-deformed two-dimensional N=(8,8) super Yang-Mills theory with preserving two supercharges exactly. Gauge fields are represented by compact unitary link variables, and the exact supercharges on the lattice are nilpotent up to gauge transformations and SU(2)_R rotations. Due to the mass deformation, the lattice model is free from the vacuum degeneracy problem, which was encountered in earlier approaches, and flat directions of scalar fields are stabilized giving discrete minima representing fuzzy S^2. Around the trivial minimum, quantum continuum theo…
We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet $λ_{a}$, $a=1,2$, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang-Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang-Mills vacuum functional, special field-dependent BRST-antiBRST transformations, with $s_{a}$-potential parameters $λ_{a}=s_{a}Λ$ induced by a finite even-…
Consequences of large $N$ volume independence are examined in conformal and confining gauge theories. In the large $N$ limit, gauge theories compactified on $\R^{d-k} \times (S^1)^k$ are independent of the $S^1$ radii, provided the theory has unbroken center symmetry. In particular, this implies that a large $N$ gauge theory which, on $\R^d$, flows to an IR fixed point, retains the infinite correlation length and other scale invariant properties of the decompactified theory even when compactified on $\R^{d-k} \times (S^1)^k$. In other words, finite volume effects are $1/N$ suppressed. In latti…
Supersymmetric effective potential of a 5D super-Yang-Mills model compactified on $S^1/Z_2$, i.e., on an interval $l$ of extra dimension, is estimated at the 1-loop level by the auxiliary field tadpole method. For the sake of infinite towers of Kaluza-Klein excitation modes of bulk fields involved in the tadpoles, there arises a definite bulk effect of linear growth of the effective potential along with the cutoff ${\mitΛ}$ which is greatly suppressed by $l$ to produce finite contributions. The minimization of the effective potential incorporating the tree potential and a Fayet-Iliopoulos $D$-…
We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N, the length of the torus L and the Z_N magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x=λNL and an angle defined in terms of the magnetic flux (λ is 't Hooft coupling). Thus, fixing the angle, the system e…
Strong coupling dynamics of Yang--Mills theories with chiral fermion content remained largely elusive despite much effort over the years. In this work, we propose a dynamical framework in which we can address non-perturbative properties of chiral, non-supersymmetric gauge theories, in particular, chiral quiver theories on $S_1 \times R_3 $. Double-trace deformations are used to stabilize the center-symmetric vacuum. This allows one to smoothly connect small-$r(S_1)$ to large-$r(S_1)$ physics ($R_4$ is the limiting case) where the double-trace deformations are switched off. In particular, occur…
We exhibit the gauge-group independence (``universality'') of all normalized non-intersecting Wilson loop expectation values in the large N limit of two-dimensional Yang-Mills theory. This universality is most easily understood via the string theory reformulation of these gauge theories. By constructing an isomorphism between the string maps contributing to normalized Wilson loop expectation values in the different theories, we prove the large N universality of these observables on any surface. The string calculation of the Wilson loop expectation value on the sphere also leads to an indicatio…
We find an explicit form for the Jacobian of arbitrary field-dependent BRST transformations in Yang-Mills theory. For the functional-integral representation of the (gauge-fixed) Yang-Mills vacuum functional, such transformations merely amount to a precise change in the gauge-fixing functional. This proves the independence of the vacuum functional under any field-dependent BRST transformation. We also give a formula for the transformation parameter functional which generates a prescribed change of gauge and evaluate it for connecting two arbitrary R_xi gauges.
We compute and analyse the low-lying spectrum of 2+1 dimensional $SU(N)$ Yang-Mills theory on a spatial torus of size $l\times l$ with twisted boundary conditions. This paper extends our previous work \cite{Perez:2013dra}. In that paper we studied the sector with non-vanishing electric flux and concluded that the energies only depend on the parameters through two combinations: $x=λN l /(4π)$ (with $λ$ the 't Hooft coupling) and the twist angle $\tilde θ$ defined in terms of the magnetic flux piercing the two-dimensional box. Here we made a more complete study and we are able to condense our re…
We present a local setup for the recently introduced BRST-invariant formulation of Yang-Mills theories for linear covariant gauges that takes into account the existence of gauge copies à la Gribov and Zwanziger. Through the convenient use of auxiliary fields, including one of the Stueckelberg type, it is shown that both the action and the associated nilpotent BRST operator can be put in local form. Direct consequences of this fully local and BRST-symmetric framework are drawn from its Ward identities: (i) an exact prediction for the longitudinal part of the gluon propagator in linear covariant…
In the present work we analyse $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills (SYM) theory in two dimensions by means of lattice simulations. The theory arises as dimensional reduction of $\mathcal{N}=1$ SYM theory in four dimensions. As in other gauge theories with extended supersymmetry, the classical scalar potential has flat directions which may destabilize numerical simulations. In addition, the fermion determinant need not be positive and this sign-problem may cause further problems in a stochastic treatment. We demonstrate that $\mathcal{N}=(2,2)$ super Yang-Mills theory has actually no …
In this work, motivated by Laplacian type center gauges in the lattice, designed to avoid the Gribov problem, we introduce a new family of gauge fixings for pure Yang-Mills theories in the continuum. This procedure separates the partition function into partial contributions associated with different sectors, containing center vortices and correlated monopoles. We show that, on each sector, the gauge fixed path-integral displays a BRST symmetry, however, it cannot be globally extended due to sector dependent boundary conditions on the ghost fields. These are nice features as they would permit t…
We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in SU(N) Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with the algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is …
Based on general considerations such as $R$-operation and Slavnov-Taylor identity we show that the effective action, being understood as Legendre transform of the logarithm of the path integral, possesses particular structure in ${\cal N} =4$ supersymmetric Yang--Mills theory for kernels of the effective action expressed in terms of the dressed effective fields. These dressed effective fields have been introduced in our previous papers as actual variables of the effective action. The concept of dressed effective fields naturally appears in the framework of solution to Slavnov-Taylor identity. …
Recent works have explored non-perturbative effects due to the existence of (infinitesimal) Gribov copies in Yang-Mills-Chern-Simons theories in three Euclidean dimensions. In particular, the removal of such copies modify the gauge field propagator by a self-consistent dynamically generated mass parameter, the Gribov parameter. Due to the interplay with the topological mass introduced by the Chern-Simons term, the propagator features a non-trivial set of phases with poles of different nature, leading to the possible interpretation of a confinfing to deconfining phase transition. Inhere, we res…
The Faddeev-Skyrme model, a modified O(3) nonlinear sigma model in three space dimensions, is known to admit topological solitons that are stabilized by the Hopf charge. The Faddeev-Skyrme model is also related to the low-energy limits of SU(2) Yang-Mills theory. Here, the model is reformulated into its gauge-equivalent expression, which turns out to be Skyrme-like. The solitonic solutions of this Skyrme-like model are analyzed by the rational map ansatz. The energy function and the Bogomolny-type lower bound of the energy are established. The generalized Faddeev-Skyrme model that originates f…
Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at long distances. We study this theory on a four- and three-torus, and analytically argue the existence of a large-small volume equivalence. For any finite mass, center symmetry unbroken phase exists at sufficiently small volume and this phase can be used to study the large-volume limit through the Eguchi-Kawai equivalence. A finite temperature version of volume independence implies that thermodynamics on R^3 x S^1 can be studied via a unitary matrix quantum mechanics on S^1, by varying the temperature. To confirm this no…
We study the pattern of chiral symmetry breaking ($χ$SB) in the $ψχη$ model (with the chiral fermion sector containing $ ψ^{\{ij\}}$, $χ_{[ij]}$, and $η_{i}^{A}$, see [1]) on $\mathbb{R}^3 \times S^{1}_{L}$ and derive implications to $\mathbb{R}^4$ physics. Center-symmetric vacua are stabilized by a double-trace deformation. With the center symmetry maintained at small $L(S^1)\ll Λ^{-1}$, i.e. at weak coupling, no phase transitions are expected in passing to large $L(S^1)\gg Λ^{-1}$ (here $Λ$ is the dynamical Yang-Mills scale). Starting with the small $L$-limit, we find the leading-order nonpe…
Coulomb gauge Yang-Mills theory within the first order formalism is considered with a view to deriving the propagator Dyson-Schwinger equations. The first order formalism is studied with special emphasis on the BRS invariance and it is found that there exists two forms of invariance - invariance under the standard BRS transform and under a second, non-standard transform. The field equations of motion and symmetries are derived explicitly and certain exact relations that simplify the formalism are presented. It is shown that the Ward-Takahashi identity arising from invariance under the non-stan…
We study a deSitter/Anti-deSitter/Poincare Yang-Mills theory of gravity in d-space-time dimensions in an attempt to retain the best features of both general relativity and Yang-Mills theory: quadratic curvature, dimensionless coupling and background independence. We derive the equations of motion for Lie algebra valued scalars and show that in the geometric optics limit they traverse geodesics with respect to the Lorentzian geometry determined by the frame fields. Mixing between components appears to next to leading order in the WKB approximation. We then restrict to two space-time dimensions …
We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in SU(N) Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is poss…
Non-commutative differential geometry allows a scalar field to be regarded as a gauge connection, albeit on a discrete space. We explain how the underlying gauge principle corresponds to the independence of physics on the choice of vacuum state, should it be non-unique. A consequence is that Yang-Mills-Higgs theory can be reformulated as a generalised Yang-Mills gauge theory on Euclidean space with a $Z_2$ internal structure. By extending the Hodge star operation to this non-commutative space, we are able to define the notion of self-duality of the gauge curvature form in arbitrary dimensions.…
A new mechanism for the radius stabilization is proposed in a 5D super-Yang-Mills model in the warped background of ${AdS}_5$. Dominant 1-loop contribution to the supersymmetric 4D effective potential is estimated to depend on the radion. The minimization of the effective potential incorporating the tree potential and a Fayet-Iliopoulos $D$-term for the gauge group U(1) reveals an interesting case that the radius is stabilized at a length corresponding to an intermediate mass scale $10^{11-13}$ GeV.
On the basis of the general considerations such as $R$-operation and Slavnov-Taylor identity we show that the effective action, being understood as Legendre transform of the logarithm of the path integral, possesses particular structure in ${\cal N} = 4$ supersymmetric Yang-Mills theory for kernels of the effective action expressed in terms of the dressed effective fields. These dressed effective fields have been introduced in our previous papers as actual variables of the effective action. The concept of dressed effective fields naturally appears in the framework of solution to Slavnov-Taylor…
We review the results of our research [A.A. Reshetnyak, IJMPA 29 (2014) 1450184; P.Yu. Moshin, A.A. Reshetnyak, Nucl. Phys. B 888 (2014) 92; P.Yu. Moshin, A.A. Reshetnyak, Phys. Lett. B 739 (2014) 110; P.Yu. Moshin, A.A. Reshetnyak, arXiv:1406.5086[hep-th]], devoted to Lagrangian quantization for gauge theories with soft BRST symmetry breaking, in particular, for various descriptions of the YM theory without Gribov copies. The cited works rely on finite BRST and BRST-antiBRST transformations, respectively, with a singlet $Λ$ and a doublet $λ_{a}$, $a=1,2$, of anticommuting Grassmann parameters…
Using the effective potential approach for composite operators, we have formulated a general method of calculation of the truly non-perturbative Yang-Mills vacuum energy density (this is, by definition, the Bag constant apart from the sign). It is the main dynamical characteristic of the QCD ground state. Our method allows one to make it free of the perturbative contributions ('contaminations'), by construction. We also perform an actual numerical calculation of the Bag constant for the confining effective charge. Its choice uniquely defines the Bag constant, which becomes free of all the type…
This doctoral work deals with the analysis of some Yang-Mills solutions on 4-dimensional de Sitter space d$S_4$. The conformal equivalence of this space with a finite Lorentzian cylinder over the 3-sphere and also with parts of Minkowski space has recently led to the discovery of a family of rational knotted electromagnetic field configurations. These "basis-knot" solutions of the Maxwell equations, aka $U(1)$ Yang-Mills theory, are labelled with the hyperspherical harmonics of the 3-sphere and have nice properties such as finite-energy, finite-action and presence of a conserved topological qu…
A qualitative study of the lightest glueball states in Euclidean SU(2) Yang-Mills theory quantized in the maximal Abelian gauge is presented. The analysis is done by generalizing to the maximal Abelian gauge the so-called replica model, already successfully introduced in the Landau gauge. As it will be shown, the gluon and ghost propagators obtained from the replica model are of the same type of those already introduced in Phys. Rev. D77, 105023 (2008) [arXiv:0801.0566], whose behavior turns out to be in agreement with that available from the lattice data on the maximal Abelian gauge. The mode…
We study the thermodynamics and dynamics of high-dimensional Einstein-power-Yang-Mills black holes in conformal gravity. Specifically, we investigate a class of conformally related black holes whose metrics differ by a scale factor. We show that a suitable scale factor cures the geodesic incompleteness and the divergence of Kretschmann scalars at the center of black holes. In the aspect of thermodynamics, we analyse the Hawking temperature, the entropy, and the specific heat, and verify the existence of second-order phase transitions. We find that the thermodynamics of this class of conformall…
A four dimensional generally covariant modified Yang-Mills action, which depends on the lorentzian complex structure of spacetime and not its metric, is presented. The extended Weyl symmetry, implied by the effective metric independence, makes the lagrangian model renormalizable. The modified Yang-Mills action generates a linear potential, instead of the Coulomb-like (1/r) potential of the ordinary action. Therefore the Yang-Mills excitations must be perturbatively confined. The metric, which admits an integrable lorentzian complex structure, can be extended to a Kaehler metric and the spaceti…
The free energy of the maximally supersymmetric SU(N) gauge theory at temperature T is expected to scale, in the large N limit, as N^2 T^4 times a function of the 't Hooft coupling, f(g_{YM}^2 N). In the strong coupling limit the free energy has been deduced from the near-extremal 3-brane geometry, and its normalization has turned out to be 3/4 times that found in the weak coupling limit. In this paper we calculate the leading correction to this result in inverse powers of the coupling, which originates from the R^4 terms in the tree level effective action of type IIB string theory. The correc…
The understanding of the non-perturbative regime of YM theories remains a challenging open problem in theoretical physics. Notably, a satisfactory description of the confinement of gluons is not at our disposal so far. In this thesis, the RGZ framework, designed to provide a proper quantization of YM theories by taking into account the existence of the so-called Gribov copies is explored. Successfully introduced in the Landau gauge, the RGZ set up does not extend easily to different gauges. The main reason is that a clear formulation of the analogue of the Gribov horizon in the Landau gauge is…
The fermionic gyromagnetic ratio g= 2 of the Kerr-Newman spacetime cannot be a computational "coincidence". This naturally immerges in a four dimensional generally covariant modified Yang-Mills action, which depends on the lorentzian complex structure of spacetime and not its metric. This metric independence makes the model renormalizable. It is a counter example to the general belief that "string theory is the only selfconsistent quantum model which includes gravity". The other properties of the model are phenomenologically very interesting too. The modified Yang-Mills action generates a line…
