Abelian Background Research Articles

Topological Gauge Actions on the Lattice as Overlap Fermion Determinants

Overlap fermion on the lattice has been shown to properly reproduce topological aspects of gauge fields. In this paper, we review the derivation of Overlap fermion formalism in a torus of three space-time dimensions. Using the formalism, we show how to use the Overlap fermion determinants in the massless and infinite mass limits to construct different continuum topological gauge actions, such as the level-k Chern–Simons action, “half-CS” term and the mixed Chern–Simons (BF) coupling, in a gauge-invariant lattice UV regulated manner. Taking special Abelian and non-Abelian background fields, we demonstrate numerically how the lattice formalism beautifully reproduces the continuum expectations, such as the flow of action under large gauge transformations.

Energy-driven disorder in mean field QCD

An impact of the finite size effects on the vacuum free energy density of full QCD with $N_{\rm f}$ massless flavors in the presence of homogeneous (anti-)self-dual Abelian background gluon field is studied. The zero temperature free energy density of the four-dimensional spherical domain is computed as a function of the background field strength $B$ and domain radius $R$. Calculation is performed in the one-loop approximation improved by accounting for mixing of the quark and gluon quasi-zero modes with normal modes, with the use of the $\zeta$-function regularization. It is indicated that, under plausible assumption on the character of the mixing, the quantum correction to the free energy density has a minimum as a function of $B$ and $R$. Within the mean field approach to QCD vacuum based on domain wall network representation of the mean field, an existence of the minimum may prevent infinite growth of individual domain, thus protecting the vacuum from the long-range ordering, and, hence, serving as the origin of disorder in the statistical ensemble of domain wall networks, driven by the minimization of the overall free energy of the dominant gauge field configurations.

Topological vortices in gauge models of graphene

Abstract Graphene-like structure possessing the topological vortices and knots, and the magnetic flux of the vortices configuration quantized, are proposed in this paper. The topological charges of the vortices are characterized by Hopf indices and Brower degrees. The Abelian background field action (BF action) is a topological invariant for the knot family, which is just the total sum of all the self-linking numbers and all the linking numbers. Flux quantization opens the possibility of having Aharonov-Bohm-type effects in graphene without external electromagnetic field.

Mesons from (non) Abelian T-dual backgrounds

In this work we study mesonic excitations in a Quantum Field Theory dual to the non Abelian T-dual of AdS5 × S5, using a D6 brane probe on the Sfetsos-Thompson background. Before and after the duality, we observe interesting differences between the spectra and interpret them. The spectrum of masses and the interactions between mesonic excitations teach valuable lessons about the character of non-Abelian T-duality and its implications for Holography. The case of Abelian T-duality is also studied.

Hydrodynamics with gauge anomaly: Variational principle and Hamiltonian formulation

We present a variational principle for relativistic hydrodynamics with gauge-anomaly terms for a fluid coupled to an Abelian background gauge field. For this we utilize the Clebsch parametrization of the velocity field. We also set up the Hamiltonian formulation and the canonical framework for the theory. While the equations of motion only involve the density and velocity fields, i.e., the Clebsch potentials only appear in the combination which is the velocity field, the generators of symmetry transformations (including the Hamiltonian) depend explicitly on one of the Clebsch potentials, if the background field is time-dependent. For the special case of time-independent background fields, this feature is absent.

Automatic generation of Feynman rules in the Schrödinger functional

We provide an algorithm to generate vertices for the Schrödinger functional with an abelian background gauge field. The background field has a non-trivial color structure, therefore we mainly focus on a manipulation of the color matrix part. We propose how to implement the algorithm especially in python code. By using python outputs produced by the code, we also show how to write a numerical expression of vertices in the time-momentum as well as the coordinate space into a Feynman diagram calculation code. As examples of the applications of the algorithm, we provide some one-loop results, ratios of the Λ parameters between the plaquette gauge action and the improved gauge actions composed from six-link loops (rectangular, chair and parallelogram), the determination of the O( a) boundary counter term to this order, and the perturbative cutoff effects of the step scaling function of the Schrödinger functional coupling constant.

Exact effective action for(1+1)-dimensional fermions in an Abelian background at finite temperature and chemical potential

In this paper we study the effects of a nonzero chemical potential in $(1+1)$-dimensional quantum field models at finite temperature. We particularly consider massless fermions in an Abelian gauge field background and calculate the effective action by evaluating the $n$-point functions. We find that the structure of the amplitudes corresponds to a generalization of the structure noted earlier in a calculation without a chemical potential (the associated integrals carry the dependence on the chemical potential). Our calculation shows that the chiral anomaly is unaffected by the presence of a chemical potential at finite temperature. However, unlike in the absence of a chemical potential, odd point functions do not vanish. We trace this to the fact that in the presence of a chemical potential the generalized charge conjugation symmetry of the theory allows for such amplitudes. In fact, we find that all the even point functions are even functions of $\ensuremath{\mu}$, while the odd point functions are odd functions of $\ensuremath{\mu}$ which is consistent with this generalized charge conjugation symmetry. We show that the origin of the structure of the amplitudes is best seen from a formulation of the theory in terms of left- and right-handed spinors. The calculations are also much simpler in this formulation and it clarifies many other aspects of the theory.

Construction of the effective action in nonanticommutative supersymmetric field theories

We develop a general gauge invariant construction of the one-loop effective action for supersymmetric gauge field theories formulated in N=1/2 superspace. Using manifestly covariant techniques (the background superfield method and proper-time representations) adopted to the N=1/2 superspace we show how to define unambiguously the effective action of a matter multiplet (in fundamental and adjoint representations) and the vector multiplet coupled to a background N=1/2 gauge superfield. As an application of this construction we exactly calculate the low-energy one-loop effective action of matter multiplet and SU(2) SYM theory on the Abelian background.

Effective action ofβ-deformedN=4SYM theory and AdS/CFT

We compute the one-loop effective action in $\mathcal{N}=1$ superconformal $SU(N)$ gauge theory which is an exactly marginal deformation of the $\mathcal{N}=4$ SYM. We consider an Abelian background of constant $\mathcal{N}=1$ gauge field and single chiral scalar. While for finite $N$ the effective action depends nontrivially on the deformation parameter $q={e}^{i\ensuremath{\pi}\ensuremath{\beta}}$, this dependence disappears in the large $N$ limit if the parameter $\ensuremath{\beta}$ is real. This conclusion matches the strong-coupling prediction coming from the form of a D3-brane probe action in the dual supergravity background: for the simplest choice of the D3-brane position the probe action happens to be the same as for a D3-brane in $Ad{S}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ placed parallel to the boundary of $Ad{S}_{5}$. This suggests that in the real $\ensuremath{\beta}$ deformation case there exists a large $N$ nonrenormalization theorem for the ${F}^{4}$ term in the action.

Edge states for quantum Hall droplets in higher dimensions and a generalized WZW model

We consider quantum Hall droplets on complex projective spaces with a combination of Abelian and non-Abelian background magnetic fields. Carrying out an analysis similar to what was done for Abelian backgrounds, we show that the effective action for the edge excitations is given by a chiral, gauged Wess–Zumino–Witten (WZW) theory generalized to higher dimensions.

Fermion determinant for general background gauge fields

An exact representation of the Euclidean fermion determinant in two dimensions for centrally symmetric, finite-ranged Abelian background fields is derived. Input data are the wave function inside the field's range and the scattering phase shift with their momenta rotated to the positive imaginary axis and fixed at the fermion mass for each partial-wave. The determinant's asymptotic limit for strong coupling and small fermion mass for square-integrable, unidirecitonal magnetic fields is shown to depend only on the chiral anomaly. The concept of duality is extended from one to two-variable fields, thereby relating the two-dimensional Euclidean determinant for a class of background magnetic fields to the pair production probability in four dimensions for a related class of electric pulses. Additionally, the ``diamagnetic'' bound on the two-dimensional Euclidean determinant is related to the negative sign of dImS_eff/dm^2 in four dimensions in the strong coupling, small mass limit, where S_eff is the one-loop effective action.

Quantum metamorphosis of conformal symmetry in N=4 super Yang–Mills theory

In gauge theories, not all rigid symmetries of the classical action can be maintained manifestly in the quantization procedure, even in the absence of anomalies. If this occurs for an anomaly-free symmetry, the effective action is invariant under a transformation that differs from its classical counterpart by quantum corrections. As shown by Fradkin and Palchik years ago, such a phenomenon occurs for conformal symmetry in quantum Yang–Mills theories with vanishing beta function, such as the N=4 super Yang–Mills theory. More recently, Jevicki et al. demonstrated that the quantum metamorphosis of conformal symmetry sheds light on the nature of the AdS/CFT correspondence. In this paper, we derive the conformal Ward identity for the bosonic sector of the N=4 super Yang–Mills theory using the background field method. We then compute the leading quantum modification of the conformal transformation for a specific Abelian background which is of interest in the context of the AdS/CFT correspondence. In the case of scalar fields, our final result agrees with that of Jevicki et al. The resulting vector and scalar transformations coincide with those which are characteristic of a D3-brane embedded in AdS 5× S 5.

Probing the Nonperturbative Dynamics of Lattice Gauge Theories

We investigate the vacuum dynamics of lattice gauge theories by means of a gaugeinvariant effective action defined through the lattice Schrodinger functional. The vacuum is probed using external background fields. An external constant Abelian chromomagnetic field and an Abelian monopole background field are considered. Numerical simulations have been performed employing APE/Quadrics computers. In the case of the Abelian monopole background field we have simulated the U(1) lattice gauge theory at zero temperature and the SU(2) and SU(3) lattice gauge theories at finite temperature. Introducing a disorder parameter that signals the Abelian monopole condensation in the confined phase, a gaugeinvariant evidence of the monopole condensation in the vacuum has been found. In the case of the external Abelian chromomagnetic background field we performed numerical simulations both at zero and finite temperature. The results suggest that at zero temperature the external field is screened in the continuum limit. On the other hand at finite temperature it seems that confinement is restored by increasing the strength of the applied field.

The Haldane-Rezayi Quantum Hall State and Magnetic Flux

We consider the general Abelian background configurations for the Haldane-Rezayi quantum Hall state. We determine the stable configurations to be the ones with the spontaneous flux of $(\mathbf{Z}+1/2){\ensuremath{\varphi}}_{0}$ with ${\ensuremath{\varphi}}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}hc/e$. This gives the physical mechanism by which the edge theory of the state becomes identical to the one for the 331 state. It also provides a new experimental consequence which can be tested in the enigmatic $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5/2$ plateau in a single-layer system.

On non-linear superfield versions of the vector-tensor multiplet

We propose a harmonic superspace description of the non-linear vector-tensor N=2 multiplet. We show that there exist two inequivalent version: the old one in which one of the vectors is the field-strength of a gauge two-form, and a new one in which this vector satisfies a non-linear constraint and cannot be expressed in terms of a potential. In this the new version resembles the non-linear N=2 multiplet. We perform the dualization of both non-linear versions and discuss the resulting K\"ahler potentials. Finally, we couple the non-linear vector-tensor multiplet to an abelian background gauge multiplet.

Finite temperature quark confinement via chromomagnetic fields

A natural mechanism for finite temperature quark confinement arises via the coupling of the adjoint.Polyakov loop to the chromamagnetic field. Lattice simulations and analytical results both support this hypothesis. Finite temperature SU(3) lattice simulations show that a large external coupling to the chromomagnetic field restores confinement at temperatures above the normal deconfining temperature. A one-loop calculation of the effective potential for SU(2) gluons in a background field shows that a constant chromomagnetic field can drive the Polyakov loop to confining behavior, and the Polyakov loop can in turn remove the well-known tachyonic mode associated with gluons in an external chromomagnetic field. For abelian background fields, tachyonic modes are necessary for confinement at one loop.

Finite temperature quark confinement

Confinement may be more easily demonstrated at finite temperature using the Polyakov loop than at zero temperature using the Wilson loop. A natural mechanism for confinement can arise via the coupling of the adjoint Polyakov loop to F_{mu nu}^2. We demonstrate this mechanism with a one-loop calculation of the effective potential for SU(2) gluons in a background field consisting of a non-zero color magnetic field and a non-trivial Polyakov loop. The color magnetic field drives the Polyakov loop to non-trivial behavior, and the Polyakov loop can remove the well-known tachyonic mode associated with the Saviddy vacuum. Minimizing the real part of the effective potential leads to confinement, as determined by the Polyakov loop. Unfortunately, we cannot arrange for simultaneous stability and confinement for this simple class of field configurations. We show for a large class of abelian background fields that at one loop tachyonic modes are necessary for confinement.

Abelian nature of cooled SU(2) lattice configurations

We introduce a gauge-invariant measure of the local ``Abelianicity'' of any given lattice configuration in non-Abelian lattice gauge theory; it is essentially a comparison of the magnitude of field strength commutators to the magnitude of the field strength itself. This measure, in conjunction with the cooling technique, is used to probe the SU(2) lattice vacuum for a possible large-scale Abelian background, underlying the local short-range field fluctuations. We do, in fact, find a substantial rise in the Abelianicity over ten cooling steps or so, after which the Abelianicity tends to drop again.

Fermion determinants and effective actions

Configuration space heat-kernel methods are used to evaluate the determinant and hence the effective action for a SU(2) doublet of fermions in interaction with a covariantly constant SU(2) background field. Exact results are exhibited that are applicable to any Abelian background on which the only restriction is that (B2−E2) and E⋅B are constant. Such fields include the uniform field and the plane wave field. The fermion propagator is also given in terms of gauge covariant objects. An extension to include finite temperature effects is given and the probability for creation of fermions from the vacuum at finite temperature in the presence of an electric field is discussed.

Fermionic Field Theory and Gauge Interactions on Random Lattices

Random-lattice fermions have been shown to be free of the doubling problem if there are no interactions or interactions of a non-gauge nature. However, gauge interactions impose stringent constraints as expressed by the Ward-Takahashi identities which could revive the free-field suppressed doubler modes in loop diagrams. After introducing a formulation for fermions on a new kind of random lattice, we compare random, naive, and Wilson fermions in two-dimensional Abelian background gauge theory. We show that the doublers are revived for random lattices in the continuum limit, while demonstrating that gauge invariance plays the critical role in this revival. Some implications of the persistent doubling phenomenon on random lattices are also discussed.