The study of Yang-Mills theories in three dimensions is an insightful playground to grasp important features for the four-dimensional case. Additionally, in three dimensions, the Chern-Simons term can be introduced with a mass parameter of topological nature. Quantizing such a theory in the continuum demands a gauge fixing which, in general, is plagued by Gribov copies. In this work, Yang-Mills-Chern-Simons theories are quantized in the maximal Abelian gauge and the existence of infinitesimal Gribov copies is taken into account. The elimination of copies modifies the (Abelian) gluon propagator leading to two different phases: one in which all poles are complex and thus interpreted as a confining phase and another where an excitation which can be part of the physical spectrum is present.
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…
In this paper we derive in a coordinate-free manner the field equations for a lagrangean consisting of Yang-Mills kinetical term plus Chern-Simons self-coupling term. This equation turns out to be an eigenvalue equation for the covariant laplacian.
We perform nonperturbative studies of the dimensionally reduced 5d Yang-Mills-Chern-Simons model, in which a four-dimensional fuzzy manifold, ``fuzzy S$^{4}$'', is known to exist as a classical solution. Although the action is unbounded from below, Monte Carlo simulations provide an evidence for a well-defined vacuum, which stabilizes at large $N$, when the coefficient of the Chern-Simons term is sufficiently small. The fuzzy S$^{4}$ prepared as an initial configuration decays rapidly into this vacuum in the process of thermalization. Thus we find that the model does not possess a ``fuzzy S$^{…
Nilpotency of the pure spinor BRST operator in a curved background implies superspace equations of motion for the background. By computing one-loop corrections to nilpotency for the heterotic sigma model, the Yang-Mills Chern-Simons corrections to the background are derived.
We consider the BPS dyonic instantons in the 5-dim supersymmetric Yang-Mills Chern-Simons theories. Its field theoretic structures and the moduli space dynamics in term of the ADHM data have been explored in detail. We find that the field theoretic Chern-Simons term leads to an effective magnetic field on instanton moduli space.
Recently, gauged supergravities in three dimensions with Yang-Mills and Chern-Simons type interactions have been constructed. In this article, we demonstrate that any gauging of Yang-Mills type with semisimple gauge group G_0, possibly including extra couplings to massive Chern-Simons vectors, is equivalent on-shell to a pure Chern-Simons type gauging with non-semisimple gauge group $G_0 \ltimes T \subset G$, where T is a certain translation group, and where G is the maximal global symmetry group of the ungauged theory. We discuss several examples.
We derive the usual first-order form of the Yang-Mills action in arbitrary dimensions by dimensional reduction from a Chern-Simons-like action. The antisymmetric tensor auxiliary field of the first-order action appears as a gauge field for the extra dimensions. The higher-dimensional geometry was introduced in our previous paper by adding dimensions "dual" to spin, as suggested by the superstring's affine Lie algebra.
We investigate finite energy solutions of Yang-Mills--Chern-Simons systems in odd spacetime dimensions, d=2n+1, with n>2. This can be carried out systematically for all n, but the cases n=3,4 corresponding to a 7,8 dimensional spacetime are treated concretely. These are static and spherically symmetric configurations, defined in a flat Minkowski background. The value of the electric charge is fixed by the Chern-Simons coupling constant.
We find wide class of exact solutions of Yang-Mills-Chern-Simons theory coupled to an external source, in terms of doubly periodic Jacobi elliptic functions. The obtained solutions include localized solitons, trigonometric solutions, pure cnoidal waves, and singular solutions in certain parameter range. Furthermore, it is observed that these solutions exist over a nonzero background.
Inspired by our previous finding that supersymmetric Yang-Mills-Chern-Simons (SYM-CS) theory dimensionally reduced to 1+1 dimensions possesses approximate Bogomol'nyi-Prasad-Sommerfield (BPS) states, we study the analogous phenomenon in the three-dimensional theory. Approximate BPS states in two dimensions have masses which are nearly independent of the Yang-Mills coupling and proportional to their average number of partons. These states are a reflection of the exactly massless BPS states of the underlying pure SYM theory. In three dimensions we find that this mechanism leads to anomalously li…
We study BPS vortex configurations in three dimensional U(N) Yang-Mills theories with Chern-Simons interaction coupled to scalar fields carrying flavor. We consider two kind of configurations: local vortices (when the number of flavors $N_f=N$), and semi-local vortices (when $N_f>N$). In both cases we carefully analyze the electric and magnetic properties and present explicit numerical solutions.
We prove that three-dimensional $N=1$ supersymmetric Yang-Mills-Chern-Simons theory is finite to all loop orders. In general this leaves open the possibility that different regularization methods lead to different finite effective actions. We show that in this model dimensional regularization and regularization by dimensional reduction yield the same effective action. Consequently, the superfield approach preserves BRS invariance for this model.
We show explicitly how BV Yang-Mills action emerges as a homotopy generalization of Chern-Simons theory from the algebraic constructions arising from String Field Theory.
We study quantum Chern-Simons theory as the large mass limit of the limit $D\to 3$ of dimensionally regularized topologically massive Yang-Mills theory. This approach can also be interpreted as a BRS-invariant hybrid regularization of Chern-Simons theory, consisting of a higher-covariant derivative Yang-Mills term plus dimensional regularization. Working in the Landau gauge, we compute radiative corrections up to second order in perturbation theory and show that there is no two-loop correction to the one-loop shift $k\rightarrow k+ c_{\scriptscriptstyle V},\,\,k$ being the bare Chern-Simons pa…
We have constructed a four-fermion theory coupled to a Yang-Mills-Chern-Simons gauge field which admits static multi-vortex solutions. This is achieved through the introduction of an anomalous magnetic interation term in addition to the usual minimal coupling, and the appropriate choice of the fermion quartic coupling constant.
The two-point gauge correlation function in Yang--Mills--Chern--Simons theory in three dimensional Euclidean space is analysed by taking into account the non-perturbative effects of the Gribov horizon. In this way, we are able to describe the confinement and de-confinement regimes, which naturally depend on the topological mass and on the gauge coupling constant of the theory.
Using holography, we compute the Chern-Simons diffusion rate of 4d gauge theories constructed by wrapping D4-branes on a circle. In the model with antiperiodic boundary conditions for fermions, we find that it scales like $T^6$ in the high-temperature phase. With periodic fermions, this scaling persists at low temperatures. The scaling is reminiscent of 6d hydrodynamic behavior even at temperatures small compared to compactification scales of the M5-branes from which the D4-branes descend. We offer a holographic explanation of this behavior by adding a new entry to the known map between D4 and…
We present a Chern-Simons action for N=2 Super-Yang-Mills theory (SYM) in 'full' N=2 superspace (hyperspace) augmented by coordinates of the internal SU(2) group and show that this action can be reduced to the usual SYM action in the Harmonic hyperspace. We also discover that the 'choice' of Harmonic hyperspace is not unique and under suitable conditions, further reduction to the well-known Projective hyperspace is possible.
It has been argued by some authors that the parent action approach cannot be used in order to establish the duality between the 2+1 Abelian and non-Abelian Self-Dual (SD) and Yang-Mills-Chern-Simons (YMCS) models for all the coupling regimes. We propose here an alternative (perturbative) point of view, and show that this equivalence can be achieved with the parent action approach.
We study spherically symmetric solutions of an $SO(5)$ Chern-Simons--Yang-Mills-Higgs system in $3+1$ dimensions. The Chern-Simons densities are defined in terms of both Yang-Mills fields and a $5$-component isomultiplet Higgs. The $SO(3)\times{SO(2)}$ solutions are analysed in a systematic way, by employing numerical methods. These finite energy configurations possess both electric and magnetic global charges, differing radically, however, from Julia-Zee dyons. When two or more of these Chern-Simons densities are present in the Lagrangian, solutions with vanishing electric charge but nonvanis…
We construct a solution of eleven dimensional supergravity corresponding to a stack of M2 branes localized at the center of a particular eight dimensional hyper-Kaehler manifold constructed by Gauntlett, Gibbons, Papadopoulos, and Townsend, generalizing the earlier construction of Cherkis and Hashimoto. In the decoupling limit, this solution is dual to a Chern-Simons/Yang-Mills/Matter theory in 2+1 dimensions with N=3 supersymmetry, which flows in the infra red to a superconformal Chern-Simons/Matter system preserving N=6,8 supersymmetry, constructed recently by Aharony, Bergman, Jafferis, and…
We study one-loop correction to the Chern-Simons coefficient $κ=k/4π$ in $N=1,2,3$ supersymmetric Yang-Mills Chern-Simons systems. In the pure bosonic case, the shift of the parameter $k$ is known to be $k\rightarrow k + c_v$, where $c_v$ is the quadratic Casimir of the gauge group. In the $N=1$ case, the fermionic contribution cancels the bosonic contribution by half and the shift is $k \rightarrow k+ c_v/2$, making the theory anomalous if $c_v$ is odd. In the $N=2,3$ cases, the fermionic contribution cancels the bosonic contribution completely and there is no correction. We also calculate th…
We observe that the string field theory actions for the topological sigma models describe higher or categorified Chern-Simons theories. These theories yield dynamical equations for connective structures on higher principal bundles. As a special case, we consider holomorphic higher Chern-Simons theory on the ambitwistor space of four-dimensional space-time. In particular, we propose a higher ambitwistor space action functional for maximally supersymmetric Yang-Mills theory.
We generalize the half-BPS Janus configuration of four-dimensional N=4 super Yang-Mills theory to allow the theta-angle, as well as the gauge coupling, to vary with position. We show that the existence of this generalization is closely related to the existence of novel three-dimensional Chern-Simons theories with N=4 supersymmetry. Another closely related problem, which we also elucidate, is the D3-NS5 system in the presence of a four-dimensional theta-angle.
We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons term on a flat spatial two-torus in the limit when the torus becomes small. The zero-modes of the fields then decouple from the non-zero modes and give rise to a spectrum of states with energies that are given by multiples of the square of the coupling constant. We discuss the determination of this low-energy spectrum, both for simply connected gauge groups and for gauge groups of adjoint type, with a few examples worked out in detail.
We apply supersymmetric discrete light-cone quantization (SDLCQ) to the study of supersymmetric Yang-Mills-Chern-Simons (SYM-CS) theory on R x S^1 x S^1. One of the compact directions is chosen to be light-like and the other to be space-like. Since the SDLCQ regularization explicitly preserves supersymmetry, this theory is totally finite, and thus we can solve for bound-state wave functions and masses numerically without renormalizing. The Chern-Simons term is introduced here to provide masses for the particles while remaining totally within a supersymmetric context. We examine the free, weak …
We prove that three-dimensional N=1 supersymmetric Yang-Mills-Chern-Simons theory is finite to all loops. This leaves open the possibility that different regularization methods give different finite effective actions. We show that for this model dimensional regularization and regularization by dimensional reduction yield the same effective action.
Geometric quantization of 2+1 dimensional pure Yang-Mills theory is studied with focusing on finite large scales. It is previously shown that (Yildirim, 2015, Int. J. Mod. Phys A, 30(7), 1550034), topologically massive Yang-Mills theory exhibits a Chern-Simons splitting behavior at large scales, similar to the topologically massive AdS gravity model in its near Chern-Simons limit. This splitting occurs as two Chern-Simons parts with levels $+k/2$ each, where $k$ is the original Chern-Simons level in the Lagrangian. In the pure Chern-Simons limit, split parts combine to give the original Chern-…
We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein--Yang-Mills--Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordstrom solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations. In addition a solution in closed form describing an extremal black hole with non-Abelian hair is found for a special value of the Chern-Simons coupling constant.
We analyze the Chern-Simons-like term generation in the CPT-odd Lorentz-violating Yang-Mills theory interacting with fermions. Moreover, we study the anomalies of this model as well as its quantum stability. The whole analysis is performed within the algebraic renormalization theory, which is independent of the renormalization scheme. In addition, all results are valid to all orders in perturbation theory. We find that the Chern-Simons-like term is not generated by radiative corrections, just like its Abelian version. Additionally, the model is also free of gauge anomalies and quantum stable.
We study the large $N$ phase diagram of an asymptotically free UV completion of $\mathcal{N}=1$ $SU(N)$ super-Yang-Mills-Chern-Simons theory coupled to a single massive fundamental scalar multiplet with a quartic superpotential coupling. We compute the effective superpotential at small gauge coupling $λ\equiv N/k$, and combine this with previous results in the literature to obtain the full phase diagram in this regime. We find that tuning the UV parameters allows us to reach various phases and fixed points of Chern-Simons theory that were recently discovered using large $N$ techniques, as well…
In this work we study the behaviour of Yang--Mills--Chern--Simons theory coupled to a Higgs field in the fundamental representation by taking into account the effects of the presence of the Gribov horizon. By analyzing the infrared structure of the gauge field propagator, both confined and de-confined regions can be detected. The confined region corresponds to the appearance of complex poles in the propagators, while the de-confined one to the presence of real poles. One can move from one region to another by changing the parameters of the theory.
By introducing an appropriate parent action and considering a perturbative approach, we establish, up to fourth order terms in the field and for the full range of the coupling constant, the equivalence between the noncommutative Yang-Mills-Chern-Simons theory and the noncommutative, non-Abelian Self-Dual model. In doing this, we consider two different approaches by using both the Moyal star-product and the Seiberg-Witten map.
A Hamiltonian analysis of Yang-Mills (YM) theory in (2+1) dimensions with a level $k$ Chern-Simons term is carried out using a gauge invariant matrix parametrization of the potentials. The gauge boson states are constructed and the contribution of the dynamical mass gap to the gauge boson mass is obtained. Long distance properties of vacuum expectation values are related to a Euclidean two-dimensional YM theory coupled to $k$ flavors of Dirac fermions in the fundamental representation. We also discuss the expectation value of the Wilson loop operator and give a comparison with previous results…
We construct the component action and supersymmetry transformations of the $\mathcal{N} = 3$ Chern-Simons-Yang-Mills theory that flows in the infra red to the $\mathcal{N} = 3$ super conformal quiver Chern-Simons gauge theory obtained by Jafferis and Tomasiello in \cite{Jafferis:2008qz}. We then obtain classical $\frac{1}{3}$-BPS (and anti-BPS) solutions all along the RG flow. The solutions display a rich structure, for example, there is a non-trivial moduli space. Various properties of supersymmetric monopole operators in the infra red super conformal field theory, such as global charges and …
We work out the relation between Chern-Simons, 2d Yang-Mills on the cylinder, and Brownian motion. We show that for the unitary, orthogonal and symplectic groups, various observables in Chern-Simons theory on S^3 and lens spaces are exactly given by counting the number of paths of a Brownian particle wandering in the fundamental Weyl chamber of the corresponding Lie algebra. We construct a fermionic formulation of Chern-Simons on $S^3$ which allows us to identify the Brownian particles as B-model branes moving on a non-commutative two-sphere, and construct 1- and 2-matrix models to compute Bro…
We derive some new relationships between matrix models of Chern-Simons gauge theory and of two-dimensional Yang-Mills theory. We show that q-integration of the Stieltjes-Wigert matrix model is the discrete matrix model that describes q-deformed Yang-Mills theory on the 2-sphere. We demonstrate that the semiclassical limit of the Chern-Simons matrix model is equivalent to the Gross-Witten model in the weak coupling phase. We study the strong coupling limit of the unitary Chern-Simons matrix model and show that it too induces the Gross-Witten model, but as a first order deformation of Dyson's ci…
In this paper we derive the universal R-matrix for the Yangian Y(u(2|2)), which is an abstract algebraic object leading to rational solutions of the Yang-Baxter equation on representations. We find that on the fundamental representation the universal R-matrix reduces to the standard rational R-matrix R = R_0(1 + P/u), where the scalar prefactor is surprisingly simple compared to prefactors one finds e.g. for sl(n) R-matrices. This leads precisely to the S-matrix giving the Bethe Ansatz of one-loop N = 4 Super Yang-Mills theory and two-loop N = 6 Chern-Simons theory.
We review work on construction of Monopoles in higher dimensions. These are solutions to a particular class of models descending from Yang--Mills systems on even dimensional bulk, with Spheres as codimensions. The topological lower bounds on the Yang-Mills action translate to Bogomol'nyi lower bounds on the residual Yang-Mills-Higgs systems. Mostly, consideration is restricted to 8 dimensional bulk systems, but extension to the arbitrary case follows systematically. After presenting the monopoles, the corresponding dyons are also constructed. Finally, new Chern-Simons densities expressed in te…
Topologically massive Yang-Mills theory is studied in the framework of geometric quantization. Since this theory has a mass gap proportional to the topological mass m, Yang-Mills contribution decays exponentially at very large distances compared to 1/m, leaving a pure Chern-Simons theory with level number k. In this paper, the near Chern-Simons limit is studied where the distance is large enough to give an almost topological theory, with a small contribution from the Yang-Mills term. It is shown that this almost topological theory consists of two copies of Chern-Simons with level number k/2, v…
We apply differential renormalization method to the study of three-dimensional topologically massive Yang-Mills and Chern-Simons theories. The method is especially suitable for such theories as it avoids the need for dimensional continuation of three-dimensional antisymmetric tensor and the Feynman rules for three-dimensional theories in coordinate space are relatively simple. The calculus involved is still lengthy but not as difficult as other existing methods of calculation. We compute one-loop propagators and vertices and derive the one-loop local effective action for topologically massive …
We use the Villain approximation to show that the Gross-Witten model, in the weak- and strong-coupling limits, is related to the unitary matrix model that describes U(N) Chern-Simons theory on S^3. The weak-coupling limit corresponds to the q->1 limit of the Chern-Simons theory while the strong-coupling regime is related to the q->0 limit. In the latter case, there is a logarithmic relationship between the respective coupling constants. We also show how the Chern-Simons matrix model arises by considering two-dimensional Yang-Mills theory with the Villain action. This leads to a U(1)^N theory w…
We use the relation between 2d Yang-Mills and Brownian motion to show that 2d Yang-Mills on the cylinder is related to Chern-Simons theory in a class of lens spaces. Alternatively, this can be regarded as 2dYM computing certain correlators in conformal field theory. We find that the partition function of 2dYM reduces to an operator of the type U=ST^pS in Chern-Simons theory for specific values of the YM coupling but finite k and N. U is the operator from which one obtains the partition function of Chern-Simons on S^3/Z_p, as well as expectation values of Wilson loops. The correspondence involv…
In this thesis, topologically massive Yang-Mills theory is studied in the framework of geometric quantization. This theory has a mass gap that is proportional to the topological mass $m$. Thus, Yang-Mills contribution decays exponentially at very large distances compared to $1/m$, leaving a pure Chern-Simons theory with level number $k$. The focus of this research is the $near$ Chern-Simons limit of the theory, where the distance is large enough to give an almost topological theory, with a small contribution from the Yang-Mills term. It is shown that this almost topological theory consists of …
We study Chern-Simons theory on 3-manifolds $M$ that are circle-bundles over 2-dimensional surfaces $Σ$ and show that the method of Abelianisation, previously employed for trivial bundles $Σ\times S^1$, can be adapted to this case. This reduces the non-Abelian theory on $M$ to a 2-dimensional Abelian theory on $Σ$ which we identify with q-deformed Yang-Mills theory, as anticipated by Vafa et al. We compare and contrast our results with those obtained by Beasley and Witten using the method of non-Abelian localisation, and determine the surgery and framing presecription implicit in this path int…
We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons term on a flat spatial two-torus. The Witten index may be computed in the weak coupling limit, where the ground state wave-functions localize on the moduli space of flat gauge connections. We perform such computations by considering this moduli space as an orbifold of a certain flat complex torus. Our results agree with those obtained previously by instead considering the moduli space as a complex projective space. An advantage of the present method is that it allows for a more straightforward determination of the discr…
Charting the different phases of Yang-Mills-Chern-Simons-Higgs theories
Instituto de Física, Facultad de Ingeniería, Universidad de la República（乌拉圭共和国大学工程学院物理研究所）；Universidade Estadual Paulista (UNESP), Faculdade de Engenharia e Ciências de Guaratinguetá（圣保罗州立大学（UNESP）瓜拉廷盖塔工程与科学学院）；CBPF - Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）
We study d=2+1 non-commutative U(1) YMCS, concentrating on the one-loop corrections to the propagator and to the dispersion relations. Unlike its commutative counterpart, this model presents divergences and hence an IR/UV mechanism, which we regularize by adding a Majorana gaugino of mass m_f, that provides (softly broken) supersymmetry. The perturbative vacuum becomes stable for a wide range of coupling and mass values, and tachyonic modes are generated only in two regions of the parameters space. One such region corresponds to removing the supersymmetric regulator (m_f >> m_g), restoring the…
We study extremal and non-extremal generalizations of the regular non-abelian solution found by Chamseddine and Volkov in 5d N=4 gauged supergravity, which has been shown by Maldacena and Nastase to describe a system of NS5-branes wrapping an three-sphere dual to three-dimensional U(N) N=1 supersymmetric Yang-Mills with Chern-Simons coupling k=N/2. All black hole solutions have a temperature larger than the Hagedorn temperature Tc of the little string theory and their entropy decreases as the temperature increases. This is a sign that the system is thermodynamically unstable above Tc. We have …
We determine the dimension of the moduli space of non-Abelian vortices in Yang-Mills-Chern-Simons-Higgs theory in 2+1 dimensions for gauge groups $G=({\rm U}(1)\times G')/\mathbb{Z}_{n_0}$ with $G'$ being an arbitrary semi-simple group and $n_0$ the greatest common divisor of the Abelian charges of the $G'$ invariants. The calculation is carried out using a Callias-type index theorem, the moduli matrix approach and a D-brane setup in Type IIB string theory. We prove that the index theorem gives the number of zeromodes or moduli of the non-Abelian vortices, extend the moduli matrix approach to …
We derive non-Abelian localization formulae for supersymmetric Yang-Mills-Chern-Simons theory with matters on a Seifert manifold M, which is the three-dimensional space of a circle bundle over a two-dimensional Riemann surface Σ, by using the cohomological approach introduced by Kallen. We find that the partition function and the vev of the supersymmetric Wilson loop reduces to a finite dimensional integral and summation over classical flux configurations labeled by discrete integers. We also find the partition function reduces further to just a discrete sum over integers in some cases, and ev…
Rényi and entanglement entropies are constructed for 2d q-deformed topological Yang-Mills theories with gauge group $U(N)$, as well as the dual 3d Chern-Simons (CS) theory on Seifert manifolds. When $q=\exp[2πi/(N+K)]$, and $K$ is odd, the topological Rényi entropy and Wilson line observables of the CS theory can be expressed in terms of the modular transformation matrices of the WZW theory, $\rm{\hat{U}(N)}_{K,N(K+N)}$. If both $K$ and $N$ are odd, there is a level-rank duality of the 2d qYM theory and of the associated CS theory, as well as that of the Rényi and entanglement entropies, and W…
We investigate static, spherically symmetric solutions of an Einstein-Yang-Mills-Chern-Simons system with negative cosmological constant, for an SO(6) gauge group. For a particular value of the Chern-Simons coefficient, this model can be viewed as a truncation of the five-dimensional maximal gauged supergravity and we expect that the basic properties of the solutions in the full model to persist in this truncation. Both globally regular, particle-like solutions and black holes are considered. In contrast with the Abelian case, the contribution of the Chern-Simons term is nontrivial already in …
