Effective Gauge Theory Research Articles

Anomalous dimensions of gauge-invariant amplitudes in massless effective gauge theories of strongly correlated systems

Anomalous dimensions of gauge-invariant amplitudes in massless effective gauge theories of strongly correlated systems

Intersecting Brane Worlds and Their Effective Interactions

In this review we describe the general geometrical framework of brane world constructions in orientifolds of type IIA string theory with D6-branes wrapping 3-cycles in a Calabi-Yau 3-fold. These branes generically intersect in points, and the patterns of intersections govern the chiral fermion spectra and issues of gauge and supersymmetry breaking in the low energy effective gauge theory on their world volume. We also specialize the discussion for the case of orbifold backgrounds with intersecting D6-branes. Then, in the second part of the paper, we discuss parts of the effective action of intersecting brane world models. Specifically we first compute from the Born-Infeld action of the wrapped D-branes the tree-level, D-term scalar potential, which is important for the stability of the considered backgrounds as well as for questions related to supersymmetry breaking. Second, we review the recent computation of one-loop gauge threshold corrections in intersecting brane world models, which are needed in order to give precise predictions for the values of the gauge couplings at low energies.

New effects in gauge theory from pp-wave superstrings

It has recently been observed that IIB string theory in the pp-wave background can be used to calculate certain quantities, such as the dimensions of BMN operators, as exact functions of the effective coupling λ′=λ/J2. These functions interpolate smoothly between the weak and strong effective coupling regimes of N=4 SYM theory at large R charge J. In this Letter we use the pp-wave superstring field theory of hep-th/0204146 to study more complicated observables. The expansion of the three-string interaction vertex suggests more complicated interpolating functions which in general give rise to fractional powers of λ′ in physical observables at weak effective coupling.

Gauge-invariant Green functions of Dirac fermions coupled to gauge fields

We develop a unified approach to both infrared and ultraviolet asymptotics of the fermion Green functions in the condensed matter systems that allow for an effective description in the framework of the Quantum Electrodynamics. By applying a path integral representation to the previously suggested form of the physical electron propagator we demonstrate that in the massless case this gauge invariant function features a "stronger-than-a-pole" branch-cut singularity instead of the conjectured Luttinger-like behavior. The obtained results alert one to the possibility that construction of physically relevant amplitudes in the effective gauge theories might prove more complex than previously thought.

Bulk and brane radiative effects in gauge theories on orbifolds

We have computed one-loop bulk and brane mass renormalization effects in a five-dimensional gauge theory compactified on the M 4×S 1/ Z 2 orbifold, where an arbitrary gauge group G is broken by the orbifold action to its subgroup H . The space–time components of the gauge boson zero modes along the H generators span the gauge theory on the orbifold fixed point branes while the zero modes of the higher-dimensional components of the gauge bosons along the G/ H generators play the role of Higgs fields with respect to the gauge group H . No quadratic divergences in the mass renormalization of the gauge and Higgs fields are found either in the bulk or on the branes. All brane effects for the Higgs field masses vanish (only wave function renormalization effects survive) while bulk effects are finite and can trigger, depending on the fermionic content of the theory, spontaneous Hosotani breaking of the brane gauge group H . For the gauge fields we do find logarithmic divergences corresponding to mass renormalization of their heavy Kaluza–Klein modes. Two-loop brane effects for Higgs field masses are expected from wave function renormalization brane effects inserted into finite bulk mass corrections.

Radiatively induced magnetic moment in four-dimensional anisotropic quantum electrodynamics in an external magnetic field

We discuss one-loop radiatively-induced magnetic moment in four-dimensional quantum electrodynamics (QED) with anisotropic coupling, and examine various cases that may be of interest in effective gauge theories of antiferromagnets, whose planar limit corresponds to highly anisotropic QED couplings. We find a different scaling with the magnetic-field intensity in case there are extra statistical gauge interactions in the model with spontaneous symmetry breaking. Such a case is encountered in the ${\mathrm{CP}}^{1}$ $\ensuremath{\sigma}\ensuremath{-}\mathrm{model}$ sector of effective spin-charge separated gauge theories of antiferromagnetic systems. Our work provides, therefore, additional ways of possible experimental probing of the gauge nature of such systems.

Electromagnetic characteristics and effective gauge theory of double-layer quantum Hall systems

The electromagnetic characteristics of double-layer quantum Hall systems are studied, with projection to the lowest Landau level taken into account and intra-Landau-level collective excitations treated in the single-mode approximation. It is pointed out that dipole-active excitations, both elementary and collective, govern the long-wavelength features of quantum Hall systems. In particular, the presence of the dipole-active interlayer out-of-phase collective excitations, inherent to double-layer systems, modifies the leading O(k) and O(k^{2}) long-wavelength characteristics (i.e., the transport properties and characteristic scale) of the double-layer quantum Hall states substantially. We apply bosonization techniques and construct from such electromagnetic characteristics an effective theory, which consists of three vector fields representing the three dipole-active modes, one interlayer collective mode and two inter-Landau-level cyclotron modes. This effective theory properly incorporates the spectrum of collective excitations on the right scale of the Coulomb energy and, in addition, accommodates the favorable transport properties of the standard Chern-Simons theories.

The structure of maximally supersymmetric Yang-Mills theory: constraining higher-order corrections

We solve the superspace Bianchi identities for ten-dimensional supersymmetric Yang-Mills theory without imposing any kind of constraints apart from the standard conventional one. In this way we obtain a set of algebraic conditions on certain fields which in the on-shell theory are constructed as composite ones out of the physical fields. These conditions must hence be satisfied by any kind of theory in ten dimensions invariant under supersymmetry and some, abelian or non-abelian, gauge symmetry. Deformations of the ordinary SYM theory (as well as the fields) are identified as elements of a certain spinorial cohomology, giving control over field redefinitions and the distinction between physically relevant higher-order corrections and those removable by field redefinitions. The conditions derived severely constrain theories involving F^2-level terms plus higher-order corrections, as for instance those derived from open strings as effective gauge theories on D-branes.

Instantons, compactification and S-duality in Script N = 4 SUSY Yang-Mills theory I

We study N=4 supersymmetric Yang-Mills (SYM) theory with gauge group SU(2) compactified to three dimensions on a circle of circumference beta. The eight fermion terms in the effective action on the Coulomb branch are determined exactly, for all beta, assuming the existence of an interacting Spin(8) invariant fixed point at the origin. The resulting formulae are manifestly invariant under the SL(2,Z) duality of four dimensional N=4 SYM and lead to interesting quantitative predictions for instanton effects in gauge theory and in Type II string theory.

Branes on group manifolds, gluon condensates, and twisted K-theory

In this work we study the dynamics of branes on group manifolds G deep in the stringy regime. After giving a brief overview of the various branes that can be constructed within the boundary conformal field theory approach, we analyze in detail the condensation processes that occur on stacks of such branes. At large volume our discussion is based on certain effective gauge theories on non-commutative `fuzzy' spaces. Using the `absorption of the boundary spin'-principle which was formulated by Affleck and Ludwig in their work on the Kondo model, we extrapolate the brane dynamics into the stringy regime. For supersymmetric theories, the resulting condensation processes turn out to be consistent with the existence of certain conserved charges taking values in some non-trivial discrete abelian groups. We obtain strong constraints on these charge groups for G = SU(N). The results may be compared with a recent proposal of Bouwknegt and Mathai according to which charge groups on curved spaces X (with a non-vanishing NSNS 3-form field strength H) are given by the twisted K-groups K*_H(X).

Renormalizable Abelian-Projected Effective Gauge Theory Derived from Quantum Chromodynamics

We show that an effective Abelian gauge theory can be obtained as a renormalizable theory from QCD in the maximal Abelian gauge. The derivation improves in a systematic manner the previous version that was obtained by one of the authors and was referred to as the Abelian-projected effective gauge theory. This result supports the view that we can construct an effective Abelian gauge theory from QCD without losing characteristic features of the original non-Abelian gauge theory. In fact, it is shown that the effective coupling constant in the resulting renormalizable theory has a renormalization-scale dependence governed by the $\beta$-function that is exactly the same as that of the original Yang-Mills theory, irrespective of the choice of gauge fixing parameters of the maximal Abelian gauge and the parameters used for identifying the dual variables. Moreover, we evaluate the anomalous dimensions of the fields and parameters in the resultant theory. By choosing the renormalized parameters appropriately, we can switch the theory into an electric or a magnetic theory.

The Principles of Gauging

The aim of this paper is twofold: First, to present an examination of the principles underlying gauge field theories. I shall argue that there are two principles directly connected to the two well-known theorems of Emmy Noether concerning global and local symmetries of the free matter-field Lagrangian, in the following referred to as “conservation principle” and “gauge principle.” Since both express nothing but certain symmetry features of the free field theory, they are not sufficient to derive a true interaction coupling to a new gauge field. For this purpose it is necessary to advocate a third, truly empirical principle which may be understood as a generalization of the equivalence principle. The second task of the paper is to deal with the ontological question concerning the reality status of gauge potentials in the light of the proposed logical structure of gauge theories. A nonlocal interpretation of topological effects in gauge theories and, thus, the non-reality of gauge potentials in accordance with the generalized equivalence principle will be favored.

Non-Abelian Stokes Theorem and Quark Confinement in SU(N) Yang-Mills Gauge Theory

We derive a new version of the non-Abelian Stokes theorem for the Wilson loop in the SU(N) case by making use of the coherent state representation on the coset space SU(N)/U(1)N−1 = FN−1, the flag space. We consider the SU(N) Yang-Mills theory in the maximal Abelian gauge in which SU(N) is broken down to U(1)N−1. First, we show that the Abelian dominance in the string tension follows from this theorem and the Abelian-projected effective gauge theory that was derived by one of the authors. Next (but independently), combining the non-Abelian Stokes theorem with a novel reformulation of the Yang-Mills theory recently proposed by one of the authors, we proceed to derive the area law of the Wilson loop in four-dimensional SU(N) Yang-Mills theory in the maximal Abelian gauge. Owing to dimensional reduction, the planar Wilson loop at least for the fundamental representation in four-dimensional SU(N) Yang-Mills theory can be estimated by the diagonal (Abelian) Wilson loop defined in the two-dimensional CPN−1 model. This derivation shows that the fundamental quarks are confined by a single species of magnetic monopole. The origin of the area law is related to the geometric phase of the Wilczek-Zee holonomy for U(N−1). The calculations are performed using the instanton calculus (in the dilute instanton-gas approximation) and using the large N expansion (in the leading order).

Abelian dominance in low-energy gluodynamics due to dynamical mass generation

We show that off-diagonal gluons and off-diagonal ghosts acquire their masses dynamically in QCD if the maximal Abelian gauge is adopted. This result strongly supports the Abelian dominance in low-energy region of QCD. The mass generation is shown to occur due to ghost–anti-ghost condensation caused by attractive quartic ghost interactions within the Abelian projected effective gauge theory (derived by one of the authors). In fact, the quartic ghost interaction is indispensable for the renormalizability due to nonlinearity of the maximal Abelian gauge. The ghost–anti-ghost condensation is associated with the spontaneous breaking of global SL(2,R) symmetry recently found by Schaden at least for SU(2) case. Moreover we write down a new extended BRS algebra in the maximal Abelian gauge which should be compared with that of Nakanishi–Ojima for the Lorentz gauge. Finally, we argue that the mass generation may be related to the spontaneous breaking of a supersymmetry OSp(4|2) hidden in the maximal Abelian gauge.

Robustness of quintessence

Recent observations seem to suggest that our Universe is accelerating, implying that it is dominated by a fluid whose equation of state is negative. Quintessence is a possible explanation. In particular, the concept of tracking solutions permits us to address the fine-tuning and coincidence problems. We study this proposal in the simplest case of an inverse power potential and investigate its robustness to corrections. We show that quintessence is not affected by the one-loop quantum corrections. In the supersymmetric case where the quintessential potential is motivated by nonperturbative effects in gauge theories, we consider the curvature effects and the K\ahler corrections. We find that the curvature effects are negligible while the K\ahler corrections modify the early evolution of the quintessence field. Finally we study the supergravity corrections and show that they must be taken into account as $Q\ensuremath{\approx}{m}_{\mathrm{Pl}}$ at small redshifts. We discuss simple supergravity models exhibiting the quintessential behavior. In particular, we propose a model where the scalar potential is given by $V(Q)=({\ensuremath{\Lambda}}^{4+\ensuremath{\alpha}}{/Q}^{\ensuremath{\alpha}}{)e}^{(\ensuremath{\kappa}{/2)Q}^{2}}.$ We argue that the fine-tuning problem can be overcome if $\ensuremath{\alpha}g~11.$ This model leads to ${\ensuremath{\omega}}_{Q}\ensuremath{\approx}\ensuremath{-}0.82$ for ${\ensuremath{\Omega}}_{\mathrm{m}}\ensuremath{\approx}0.3$ which is in good agreement with the presently available data.

The world as a dual Josephson junction

We examine some of the implications of the field-theoretical mechanism for the localization of gauge fields on hypersurfaces in higher-dimensional bulk space-time. This mechanism exploits the analogy between confinement and dual superconductivity. In the simplest case of a photon localized on a (2+1)-dimensional surface in a (3+1)-dimensional bulk, we argue that the system behaves like a dual Josephson junction. This implies that the effective gauge theory on the surface is not free, but displays weak confinement with a linear potential. We comment on the relevance of our results for the realistic case of a (3+1)-dimensional surface in a space-time with one or more extra dimensions.

Aspects of type 0 string theory

A construction of compact tachyon-free orientifolds of non-supersymmetric type 0B string theory is presented. Moreover, we study effective non-supersymmetric gauge theories arising on self-dual D3-branes in type 0B orbifolds and orientifolds.

Computation of functional integrals in problems of quantum and statistical physics

A method for computation of characteristics in quantum and statistical physics is described. This method is based on the representation of the matrix element of the evolution operator in Euclidean metrics in the form of a functional integral with a certain measure in the corresponding space and on the use of approximation formulas which we constructed for this kind of integral. No simplifying assumptions such as semiclassical approximation, no introduction of “short-time” propagators are necessary. The method is applied to the numerical study of some potential nuclear models and to investigation of the topological effects in gauge theories. The comparison of results with experimental data and with the values obtained by other authors are presented.

Quark confinement and deconfinement in QCD from the viewpoint of Abelian-projected effective gauge theory

We give another derivation of quark confinement in QCD from the viewpoint of the low-energy effective Abelian gauge theory of QCD obtained via Abelian projection. It is based on the recently discovered Berezinskii-Kosterlitz-Thouless phase transition in the four-dimensional Abelian gauge theory. Moreover, we show that there exists a critical gauge coupling constant in QCD, above which confinement set in and below which there is no confinement. In a SU( N) gauge theory with N f flavored fermions, we argue that this leads to a critical value of fermion flavors N f c for the confinement as well as the chiral symmetry breaking, which separates the deconfining and chiral symmetric phase from the confining and chiral symmetry breaking phase. A finite-temperature deconfinement transition is also discussed briefly.

Instantons in partially broken gauge groups

We discuss the effects of instantons in partially broken gauge groups on the low-energy effective gauge theory. Such effects arise when some of the instantons of the original gauge group G are no longer contained in (or can not be gauge rotated into) the unbroken group H. In cases of simple G and H, a good indicator for the existence of such instantons is the “index of embedding.” However, in the general case one has to examine π 3( G/ H) to decide whether there are any instantons in the broken part of the gauge group. We give several examples of supersymmetric theories where such instantons exist and leave their effects on the low-energy effective theory.