Naser Ahmadiniaz, Victor Miguel Banda Guzman, Christian Schubert, Fiorenzo Bastianelli, Olindo Corradini, James P. Edwards
We describe progress applying the \textit{Worldline Formalism} of quantum field theory to the fermion propagator dressed by $N$-photons to study multi-linear Compton scattering processes, explaining how this approach -- whose calculational advantages are well-known at multi-loop order -- yields compact and manifestly gauge invariant scattering amplitudes.
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Gauge theories play a fundamental role in particle physics, nuclear physics, and cosmology. The basic idea of these theories is that the Lagrangian density should be invariant under some transformations. Lagrangian invariance implies a certain freedom in defining gauge fields. In this study, the standard path integral quantization formalism is used. Gauge degrees of freedom manifest themselves in the difficulties in obtaining gauge field propagators. For a consistent quantization, it is necessary to eliminate non-physical gauge degrees of freedom. The standard procedure is to break the gauge s…
In the usual and current understanding of planar gauge choices for Abelian and non Abelian gauge fields, the external defining vector $n_μ$ can either be space-like ($n^2<0$) or time-like ($n^2>0$) but not light-like ($n^2=0$). In this work we propose a light-like planar gauge that consists in defining a modified gauge-fixing term, $\cal{L}_{GF}$, whose main characteristic is a two-degree violation of Lorentz covariance arising from the fact that four-dimensional space-time spanned entirely by null vectors as basis necessitates two light-like vectors, namely $n_μ$ and its dual $m_μ$, with $n^2…
We propose a novel prescription to take off the square root of Nambu-Goto action for a p-brane, which generalizes the Brink-Di Vecchia-Howe-Tucker or also known as Polyakov method. With an arbitrary decomposition as d+n=p+1, our resulting action is a modified d-dimensional Polyakov action which is gauged and possesses a Nambu n-bracket squared potential. We first spell out how the (p+1)-dimensional diffeomorphism is realized in the lower dimensional action. Then we discuss a possible gauge fixing of it to a direct product of $d$-dimensional diffeomorphism and n-dimensional volume preserving di…
We refine a previous proposal for obtaining the multi-instanton partition function from the supersymmetric index of the 1d supersymmetric gauge theory on the worldline of D0-branes. We provide examples where the refinements are crucial for obtaining the correct result.
The concept of gauge invariance is one of the most subtle and useful concepts in modern theoretical physics. It is one of the Standard Model cornerstones. The main benefit due to the gauge invariance is that it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every instant of time. It is the objective of this work to show a path of obtaining gauge invariant theories from non-invariant ones. Both are named also as first- and second-class theories respectively, obeying Dirac's formalism. Namely, it is very important to understand why i…
A gauge independent method of obtaining the reduced space of constrained dynamical systems is discussed in a purely lagrangian formalism. Implications of gauge fixing are also considered.
Obtaining a potential flat enough to provide slow roll inflation is often difficult when gravitational effects are included. Non-abelian discrete gauge symmetries can guarantee the flatness of the inflaton potential in this case, and also provide special field values where inflation can end.
We review the application of twist deformation formalism and the construction of noncommutative gauge theory on $κ$-Minkowski space-time. We compare two different types of twists: the Abelian and the Jordanian one. In each case we provide the twisted differential calculus and consider ${U}(1)$ gauge theory. Different methods of obtaining a gauge invariant action and related problems are thoroughly discussed.
A non-gauge dynamical system depending on parameters is considered. It is shown that these parameters can have such values that corresponding canonically quantized theory will be gauge invariant. The equations allowing to find these values of parameters are derived. The prescription under consideration is applied to obtaining the equation of motion for tachyon background field in closed bosonic string theory.
For internal gauge forces, the result of locally gauging, i.e., of performing the substitution $\partial \rightarrow D$, is physically the same whether performed on the action or on the corresponding Euler-Lagrange equations of motion. Rather unsettling, though, such commutativity fails for the standard way of coupling a Dirac fermion to the gravitational field in the setting of a local Lorentz gauge theory of general relativity in the vierbein formalism, the equivalence principle thus seemingly being here violated. This paper will present a formalism in which commutativity holds for the gravi…
In this paper, we describe a method for obtaining the nonabelian Seiberg-Witten map for any gauge group and to any order in theta. The equations defining the Seiberg-Witten map are expressed using a coboundary operator, so that they can be solved by constructing a corresponding homotopy operator. The ambiguities, of both the gauge and covariant type, which arise in this map are manifest in our formalism.
Differential cross sections of deep inelastic scattering of charged leptons from hadrons are investigated by using the gauge/string duality. We consider vector mesons derived from different holographic dual models obtaining a general expression. We focus on the strongly coupled regime of dual gauge theories for different values of the Bjorken parameter. We find new predictions which are particularly interesting for differential scattering cross sections of polarized leptons scattered off polarized vector mesons. We also carry out a detailed comparison of the moments of the structure functions …
In this work we have shown that it is possible to construct non-Abelian field theories employing, in a systematic way, the Faddeev-Jackiw symplectic formalism. This approach follows two steps. In the first step, the original Abelian fields are modified in order to introduce the non-Abelian algebra. After that, the Faddeev-Jackiw method is implemented and the gauge symmetry relative to some non-Abelian symmetry group, is introduced through the zero-mode of the symplectic matrix. We construct the SU(2) and SU(2)xU(1) Yang-Mills theories having as starting point the U(1) Maxwell electromagnetic t…
We establish a novel method of obtaining the gauge-invariant bilocal condensate of gluon fields from the solutions of the Dyson--Schwinger equations (DSE) which works in the infrared and ultraviolet limits. We present explicit results for SU(3) case in four dimensions, and compare to other related analytical and lattice results.
Our main interest here is to analyze the gauge invariance issue concerning the noncommutative relativistic particle. Since the analysis of the constraint set from Dirac's point of view classifies it as a second-class system, it is not a gauge theory. Hence, the objective here is to obtain gauge invariant actions linked to the original one. However, we have two starting points, meaning that firstly we will begin directly from the original action and, using the Noether procedure, we have obtained a specific dual (gauge invariant) action. Following another path, we will act toward the constraints…
We derive the couplings of noncommutative D-branes to spatially varying Ramond-Ramond fields, extending our earlier results in hep-th/0009101. These couplings are expressed in terms of *n products of operators involving open Wilson lines. Equivalence of the noncommutative to the commutative couplings implies interesting identities as well as an expression for the Seiberg-Witten map that was previously conjectured. We generalise our couplings to include transverse scalars, thereby obtaining a Seiberg-Witten map relating commutative and noncommutative descriptions of these scalars. RR couplings …
We derive absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the 4D free Abelian 2-form gauge theory by exploiting the superfield approach to BRST formalism. The antisymmetric tensor gauge field of the above theory was christened as the "notoph" (i.e. the opposite of "photon") gauge field by Ogievetsky and Palubarinov way back in 1966-67. We briefly outline the problems involved in obtaining the absolute anticommutativity of the (anti-) BRST transformations and their resolution within the framework of geometrical superfield approach to BRST for…
We apply the technique of sequential deconfinement to the four dimensional $\mathcal{N}\!=\!1$ $Usp(2N)$ gauge theory with an antisymmetric field and $2F$ fundamentals. The fully deconfined frame is a length-$N$ quiver. We use this deconfined frame to prove the known self-duality of $Usp(2N)$ with an antisymmetric field and $8$ fundamentals. Along the way we encounter a subtlety: in certain quivers with degenerate holomorphic operators, a naive application of Seiberg duality rules leads to an incorrect superpotential or chiral ring. We also consider the reduction to $3d$ $\mathcal{N}\!=\!2$ th…
We describe a method for obtaining analytic solutions corresponding to exact marginal deformations in open bosonic string field theory. For the photon marginal deformation we have an explicit analytic solution to all orders. Our construction is based on a pure gauge solution where the gauge field is not in the Hilbert space. We show that the solution itself is nevertheless perfectly regular. We study its gauge transformations and calculate some coefficients explicitly. Finally, we discuss how our method can be implemented for other marginal deformations.
A Hamiltonian BRST deformation procedure for obtaining consistent interactions among fields with gauge freedom is proposed. The general theory is exemplified on the three-dimensional Chern-Simons model.
We introduce topological gauge fields as nontrivial field configurations enforced by topological currents. These fields crucially determine the form of statistical gauge fields that couple to matter and transmute their statistics. We discuss the physical mechanism underlying the composite particle picture and argue that it is a duality of gauge forms that naturally relates to the notion of bosonisation in arbitrary dimensions. This is based on obtaining a generalised version of flux attachment, which yields a density-dependent gauge potential. We recover well-known results, resolve old controv…
Gauge-Invariant Scalar-Induced Gravitational Waves from Physical Observables
针对标量诱导引力波的规范依赖问题，本文提出基于 Weyl 张量磁部分或 Cotton 张量等物理可观测量并推广 Stewart-Walker 引理，证明二阶诱导引力波自动规范不变，并给出其与 Newtonian 规范结果的关系。
We present the complete four-loop four-point amplitude in N=4 super-Yang-Mills theory, for a general gauge group and general D-dimensional covariant kinematics, and including all non-planar contributions. We use the method of maximal cuts --- an efficient application of the unitarity method --- to construct the result in terms of 50 four-loop integrals. We give graphical rules, valid in D-dimensions, for obtaining various non-planar contributions from previously-determined terms. We examine the ultraviolet behavior of the amplitude near D=11/2. The non-planar terms are as well-behaved in the u…
We contextualize the improved gauge-unfixing (GU) formalism within a rather general prototypical second-class system, obtaining a corresponding first-class equivalent description enjoying gauge invariance which can be applied to several situations. The prototypical system is chosen to represent a considerable class of relevant models in field theory. By considering the improved version of the GU formalism, we show that any gauge-invariant function can be obtained in terms of a specific deformation in phase space, benefiting thus from the fact that no auxiliary variables are needed in the proce…
We study polarized deep inelastic scattering of charged leptons from spin-$1/2$ hadrons at low values of the Bjorken parameter and large 't Hooft coupling in terms of the gauge/string theory duality. We calculate the structure functions from type IIB superstring theory scattering amplitudes. We discuss the role of the non-Abelian Chern-Simons term and the Pauli term from the five-dimensional $SU(4)$ gauged supergravity. Furthermore, the exponentially small-$x$ regime where Regge physics becomes important is analyzed in detail for the antisymmetric structure functions. In this case the holograp…
The issue of space time gauge invariance for the bosonic string has been earlier addressed using the loop variable formalism. In this paper the question of obtaining a gauge invariant action for the open bosonic string is discussed. The derivative w.r.t $ln a$ (where $a$ is a world sheet cutoff) of the partition function - which is first normalized by dividing by the integral of the two point function of a marginal operator - is a candidate for the action. Applied to the zero-momentum tachyon it gives a tachyon potential that is similar to those that have been obtained using Witten's backgroun…
Using the general notions of Batalin, Fradkin, Fradkina and Tyutin to convert second class systems into first class ones, we present a gauge invariant formulation of the massive Yang-Mills theory by embedding it in an extended phase space. The infinite set of correction terms necessary for obtaining the involutive constraints and Hamiltonian is explicitly computed and expressed in a closed form. It is also shown that the extra fields introduced in the correction terms are exactly identified with the auxiliary scalars used in the generalized Stückelberg formalism for converting a gauge noninvar…
In this paper, we show the existence of magnetic monopoles in the pure $SU(2)$ Yang--Mills theory even in absence of scalar fields when the gauge-invariant mass term is introduced. This result follows from the recent proposal for obtaining the gauge field configurations in the Yang-Mills theory from the solutions of the field equations in the "complementary" gauge-scalar model with the radial length of the scalar field being fixed. The gauge-invariant mass term is obtained through a change of variables and a gauge-independent description of the Brout-Englert-Higgs mechanism which neither relie…
In this paper, we explicitly construct string theory backgrounds that realise the so-called $\mathcal N=2^\star$ gauge theory. We prove the consistency of our models by calculating their partition function and obtaining the correct gauge theory spectrum. We further provide arguments in favour of the universality of our construction which covers a wide class of models all of which engineer the same gauge theory. We reproduce the corresponding Nekrasov partition function once the $Ω$-deformation is included and the appropriate field theory limit taken. This is achieved by calculating the topolog…
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