SYM N=4 in light-cone gauge and the "bridge" identities

The solution to Slavnov-Taylor identities in D4 N=1 SYM

D4 N=1 SYM with an arbitrary chiral background superfield as the gauge coupling is considered. The solution to Slavnov-Taylor identities has been given. It has been shown that the solution is unique and allows us to restrict the gauge part of the effective action. Under the effective action in this paper we mean the 1PI diagram generator.

Not a prescription but an identity: Mandelstam-Leibbrandt

After some considerations and coincidences that appear when working in the light-cone gauge, in both the Mandelstam-Leibbrandt prescription and the covariantization method, we suspect that there must be some connection between them. This work shows that we were right and it is practically trivial to demonstrate that relationship. And since the covariantization method is not a prescription, this implies that the results of Mandelstam and Leibbrandt are not prescriptions too, but they are a identities from light-cone gauge coordinates.

Noether's Second Theorem and Ward Identities for Gauge Symmetries

Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We use Noether's second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether's second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gra…

Light-Cone Quantized QCD and Novel Hadron Phenomenology

I review progress made in solving gauge theories such as collinear quantum chromodynamics using light-cone Hamiltonian methods. I also show how the light-cone Fock expansion for hadron wavefunctions can be used to compute operator matrix elements such as decay amplitudes, form factors, distribution amplitudes, and structure functions, and how it provides a tool for exploring novel features of QCD. I also review commensurate scale relations, leading-twist identities which relate physical observables to each other, thus eliminating renormalization scale and scheme ambiguities in perturbative QCD…

Gauge compensating transformations for boosted axially symmetric membranes and light cone reductions

Some explicit examples are given for gauge compensating transformations and explicit forms of axially symmetric membrane solutions

来自共形缺陷对称性破缺的积分恒等式

Integral Identities from Symmetry Breaking of Conformal Defects

本文利用缺陷共形流形几何与破缺生成元 Lie 代数，建立缺陷算符积分四点函数与两点函数之间的恒等式，并以 N=4 SYM 的 1/2 BPS Maldacena-Wilson 圈为例验证。

Superconformal Ward Identities and their Solution

Superconformal Ward identities are derived for the the four point functions of chiral primary BPS operators for $\N=2,4$ superconformal symmetry in four dimensions. Manipulations of arbitrary tensorial fields are simplified by introducing a null vector so that the four point functions depend on two internal $R$-symmetry invariants as well as two conformal invariants. The solutions of these identities are interpreted in terms of the operator product expansion and are shown to accommodate long supermultiplets with free scale dimensions and also short and semi-short multiplets with protected dime…

Ward Identities for the 2PI effective action in QED

We study the issue of symmetries and associated Ward-like identities in the context of two-particle-irreducible (2PI) functional techniques for abelian gauge theories. In the 2PI framework, the $n$-point proper vertices of the theory can be obtained in various different ways which, although equivalent in the exact theory, differ in general at finite approximation order. We derive generalized (2PI) Ward identities for these various $n$-point functions and show that such identities are exactly satisfied at any approximation order in 2PI QED. In particular, we show that 2PI-resummed vertex functi…

Lorentz Symmetry of Supermembrane in Light Cone Gauge Formulation

We prove the Lorentz symmetry of supermembrane theory in the light cone gauge to complete the program initiated by de Wit, Marquard and Nicolai. We give some comments on extending the formulation to the M(atrix) theory.

Noether Identities, $β$-functions and symmetries in DFT

Given the $β$ functions of the closed string sigma model up to one loop in $α'$, the effective action implement the condition $β=0$ to preserve conformal symmetry at quantum level. One of the more powerful and striking results of string theory is that this effective action contains Einstein gravity as an emergent dynamics in space-time. We show from the $β$ functions and its relation with the equations of motion of the effective action, that the differential identities [1] are the Noether identities associated with the effective action and its gauge symmetries. From here, we reconstruct the ga…

Beyond Symmetries : Anomalies in Transverse Ward--Takahashi Identities

Anomalies in transverse Ward--Takahashi identities are studied, allowing discussion of the feasibility of anomalies arising in general non-symmetry Ward--Takahashi identities. We adopt the popular Fujikawa's method and rigorous dimensional renormalization to verify the existence of transverse anomalies to one-loop order and any loop order, respectively. The arbitrariness of coefficients of transverse anomalies is revealed, and a way out is also proposed after relating transverse anomalies to Schwinger terms and comparing symmetry and non-symmetry anomalies. Papers that claim the non-existence …

Unitarity, BRST Symmetry and Ward Identities in Orbifold Gauge Theories

We discuss the use of BRST symmetry and the resulting Ward identities for orbifold gauge theories as consistency checks in an arbitrary number of dimensions. We verify that both the usual orbifold symmetry breaking and the recently proposed Higgsless symmetry breaking are consistent with the nilpotency of the BRST transformation. Imposing the Ward identities resulting from the BRST symmetry on the 4-point functions of theory, we obtain relations on the coupling constants that are shown to be equivalent to the conditions for tree level unitarity. We present the complete set of these sum rules a…

Path description of coordinate-space amplitudes

We develop a coordinate version of light-cone-ordered perturbation theory, for general time-ordered products of fields, by carrying out integrals over one light-cone coordinate for each interaction vertex. The resulting expressions depend on the lengths of paths, measured in the same light-cone coordinate. Each path is associated with a denominator equal to a "light-cone deficit", analogous to the "energy deficits" of momentum-space time- or light-cone-ordered perturbation theory. In effect, the role played by intermediate states in momentum space is played by paths between external fields in …

Fully developed isotropic turbulence: symmetries and exact identities

We consider the regime of fully developed isotropic and homogeneous turbulence of the Navier-Stokes equation with a stochastic forcing. We present two gauge symmetries of the corresponding Navier-Stokes field theory, and derive the associated general Ward identities. Furthermore, by introducing a local source bilinear in the velocity field, we show that these symmetries entail an infinite set of exact and local relations between correlation functions. They include in particular the Kármán-Howarth relation and another exact relation for a pressure-velocity correlation function recently derived …

Gauge symmetry and Slavnov-Taylor identities for randomly stirred fluids

The path integral for randomly forced incompressible fluids is shown to have an underlying Becchi-Rouet-Stora (BRS) symmetry as a consequence of Galilean invariance. This symmetry must be respected to have a consistent generating functional, free from both an overall infinite factor and spurious relations amongst correlation functions. We present a procedure for respecting this BRS symmetry, akin to gauge fixing in quantum field theory. Relations are derived between correlation functions of this gauge fixed, BRS symmetric theory, analogous to the Slavnov-Taylor identities of quantum field theo…