Gauge Invariant Operators Research Articles

Top Effective Operators at the ILC

In this paper we study the effect of new physics contributions to the top quark pair production (tt̄) in a possible future linear collider, such as the International Linear Collider (ILC). The use of a dimension-six gauge invariant effective operator approach allows to compare the prospected results at the ILC with the current ones obtained at the Large Hadron Collider (LHC), both in neutral and charged current processes. We also prove that the use of specific observables, together with a combination of measurements in different polarized beam scenarios and with different center-of-mass energies, allows to disentangle different effective operator contributions and significantly improve the limits on the anomalous couplings with respect to the LHC.

On a discrete symmetry of the Bremsstrahlung function in $ \mathcal{N} $ = 4 SYM

We consider the quark anti-quark potential on the three sphere in planar N = 4 SYM and the associated vacuum potential in the near BPS limit with L units of R-charge. The associated Bremsstrahlung function BL has been recently computed analytically by means of the Thermodynamical Bethe Ansatz. We discuss it at strong coupling by computing it at large but nite L. We provide strong support to a special symmetry of the Bremsstrahlung function under the formal discrete Z2 symmetry L ! 1 L. In this context, it is the counterpart of the reciprocity invariance discovered in the past in the spectrum of various gauge invariant composite operators. The Z2 symmetry has remarkable consequences in the scaling limit where L is taken to be large with xed ratio to the 't Hooft coupling. This limit organizes in inverse powers of the coupling and resembles the semiclassical expansion of the dual string theory which is indeed known to capture the leading classical term. We show that the various higher-order contributions to the Bremsstrahlung function obey several constraints and, in particular, the next-to-leading term, formally associated with the string one-loop correction, is completely determined by the classical contribution. The large L limit at strong coupling is also discussed.

Gauge invariant descriptions of gluon polarizations revisited

We examine the feasibility of gauge invariant descriptions of the gluon polarization following the proposal that a gauge field can be decomposed into its physical part and its pure gauge part. We show that gauge invariant angular momentum currents can be constructed from summations of gauge variant Noether currents. We present novel expressions of the pure gauge field, which are used to formulate gauge invariant descriptions of the gluon spin and the photon spin. We show that the gauge invariant extension of the Chern-Simons current can describe the spins of the Laguerre-Gauss laser modes. We also discuss the relation of gauge invariant operators and the parton distributions constructed from Dirac variables.

Holonomy operator and quantization ambiguities on spinor space

We construct the holonomy-flux operator algebra in the recently developed spinor formulation of loop gravity. We show that, when restricting to SU(2)-gauge invariant operators, the familiar grasping and Wilson loop operators are written as composite operators built from the gauge-invariant ``generalized ladder operators'' recently introduced in the $\mathrm{U}(N)$ approach to intertwiners and spin networks. We comment on quantization ambiguities that appear in the definition of the holonomy operator and use these ambiguities as a toy model to test a class of quantization ambiguities which is present in the standard regularization and definition of the Hamiltonian constraint operator in loop quantum gravity.

NONPLANAR INTEGRABILITY AND PARITY IN ABJ THEORY

In this paper, we study the action of the nonplanar two-loop dilatation operator in an SU(2)×SU(2) subsector of the ABJ Chern–Simons-matter theory. The gauge invariant operators we consider are the restricted Schur polynomials. As in ABJM theory, there is a limit in which the spectrum reduces to a set of decoupled harmonic oscillators, indicating integrability in the large M and N double limit of the theory. We then consider parity transformations on the gauge invariant operators. In this case the nonplanar anomalous dimensions break parity invariance. Our analysis shows that (M-N) is related to the holonomy in the string theory, confirming one of the main features of the theory and its string dual. Furthermore, in the limit where ABJ theory reduces to ABJM theory, parity invariance is restored.

Origin of neutrino masses at the LHC:ΔL=2effective operators and their ultraviolet completions

Neutrino masses and mixings can be generated in many different ways, with some of these scenarios featuring new physics at energy scales relevant for Large Hadron Collider searches. A systematic approach to constructing a large class of models for Majorana neutrinos may be founded upon a list of gauge-invariant effective operators---formed from quarks, leptons and the Higgs doublet---that violate lepton-number conservation by two units. By opening up these operators in all possible ways consistent with some minimality assumptions, a complete catalog of a class of minimal radiative neutrino mass models may be produced. In this paper we present an analysis of Feynman diagram topologies relevant for the ultraviolet completions of these effective operators and collect these into a simple recipe that can be used to generate radiative neutrino mass models. Since high mass-dimension effective operators are suppressed by powers of the scale of new physics, many of the resulting models can be meaningfully tested at the Large Hadron Collider.

Quivers as calculators: counting, correlators and Riemann surfaces

The spectrum of chiral operators in supersymmetric quiver gauge theories is typically much larger in the free limit, where the superpotential terms vanish. We find that the finite N counting of operators in any free quiver theory, with a product of unitary gauge groups, can be described by associating Young diagrams and Littlewood-Richardson multiplicities to a simple modification of the quiver, which we call the split-node quiver. The large N limit leads to a surprisingly simple infinite product formula for counting gauge invariant operators, valid for any quiver with bifundamental fields. An orthogonal basis for the operators, in the finite N CFT inner product, is given in terms of quiver characters. These are constructed by inserting permutations in the split-node quivers and interpreting the resulting diagrams in terms of symmetric group matrix elements and branching coefficients. The fusion coefficients in the chiral ring - valid both in the UV and in the IR - are computed at finite N. The derivation follows simple diagrammatic moves on the quiver. The large N counting and correlators are expressed in terms of topological field theories on Riemann surfaces obtained by thickening the quiver. The TFTs are based on symmetric groups and defect observables associated with subgroups play an important role. We outline the application of the free field results to the construction of BPS operators in the case of non-zero super-potential.

Phase with no mass gap in nonperturbatively gauge-fixed Yang-Mills theory

An equivariantly gauge-fixed non-Abelian gauge theory is a theory in which a coset of the gauge group, not containing the maximal Abelian subgroup, is gauge fixed. Such theories are nonperturbatively well defined. In a finite volume, the equivariant Becchi-Rouet-Stora-Tyutin symmetry guarantees that expectation values of gauge-invariant operators are equal to their values in the unfixed theory. However, turning on a small breaking of this symmetry, and turning it off after the thermodynamic limit has been taken, can in principle reveal new phases. In this paper we use a combination of strong-coupling and mean-field techniques to study an $SU(2)$ Yang-Mills theory equivariantly gauge fixed to a $U(1)$ subgroup. We find evidence for the existence of a new phase in which two of the gluons becomes massive while the third one stays massless, resembling the broken phase of an $SU(2)$ theory with an adjoint Higgs field. The difference is that here this phase occurs in an asymptotically free theory.

Correlation functions of local composite operators from generalized unitarity

We describe the use of generalized unitarity for the construction of correlation functions of local gauge-invariant operators in general quantum field theories and illustrate this method with several calculations in N=4 super-Yang-Mills theory involving BPS and non-BPS operators. Form factors of gauge-invariant operators and their multi-operator generalization play an important role in our construction. We discuss various symmetries of the momentum space presentation of correlation functions, which is natural in this framework and give examples involving non-BPS and any number of BPS operators. We also discuss the calculation of correlators describing the energy flow in scattering processes as well as the construction of the effective action of a background gravitational field.

On the Spectrum of Lattice Massive SU(2) Yang–Mills

On the basis of extended simulations we provide some results concerning the spectrum of Massive SU(2) Yang-Mills on the lattice. We study the "time" correlator of local gauge invariant operators integrated over the remaining three dimensions. The energy gaps are measured in the isospin I=0,1 and internal spin J=0,1 channels. No correlation is found in the I=1,J=0 channel. In the I=1, J=1 channel and far from the critical mass value $m_c$ the energy gap roughly follows the bare value $m$ (vector mesons). In approaching the critical value $m_c$ at $\beta$ fixed, there is a bifurcation of the energy gap: one branch follows the value $m$, while the new is much larger and it shows a more and more dominant weight. This phenomenon might be the sign of two important features: the long range correlation near the fixed point at $\beta \to \infty$ implied by the low energy gap and the screening (or confining) mechanisms across the $m=m_c$ associated to the larger gap. The I=0, J=0,1 gaps are of the same order of magnitude, typically larger than the I=1, J=1 gap (for $m>>m_c$). For $m\sim m_c$ both I=0 gaps have a dramatic drop with minima near the value $m$. This behavior might correspond to the formation of I=0 bound states both in the J=0 and J=1 channels.

Transverse Parton Distribution Functions at Next-to-Next-to-Leading Order: The Quark-to-Quark Case

We present a calculation of the perturbative quark-to-quark transverse parton distribution function at next-to-next-to-leading order based on a gauge invariant operator definition. We demonstrate for the first time that such a definition works beyond the first nontrivial order. We extract from our calculation the coefficient functions relevant for a next-to-next-to-next-to-leading logarithmic Q(T) resummation in a large class of processes at hadron colliders.

Exceptional operators in $ \mathcal{N} = 4 $ super Yang-Mills

We consider one particularly interesting class of composite gauge-invariant operators in $ \mathcal{N} = 4 $ super Yang-Mills theory. An exceptional feature of these operators is that in the Thermodynamic Bethe Ansatz approach the one-loop rapidities of the constituent magnons are shown to be exact in the ’t Hooft coupling constant. This is used to propose the mirror TBA description for these operators. The proposal is shown to pass several non-trivial checks.

Optimal-observable analysis of possible non-standard top-quark couplings in [formula omitted

Possible non-standard top-quark interactions with the gluon and the W boson induced by SU(3)×SU(2)×U(1) gauge-invariant dimension-6 effective operators are studied for hadron-collider experiments. Current limits on top-gluon couplings are presented by using the latest experimental data of tt¯ productions at the Tevatron and the Large Hadron Collider (LHC). The optimal-observable procedure is applied to the charged-lepton distributions in pp→tt¯X→ℓ+X′ (ℓ=e or μ) at the LHC in order to estimate the expected statistical uncertainties in measurements of those non-standard top-gluon and top-W couplings that contribute to this process in the leading order.

Correlation functions and representation bases in free [formula omitted] super Yang–Mills

We study exact correlation functions of N=4 SYM at zero coupling. It has been known that it is convenient to label local gauge invariant operators by irreducible representations of symmetric groups/Brauer algebras. We first review the construction of representation bases from the viewpoint of the enhanced symmetry structure of the free theory. We present a basis of multi-matrix models using elements of Brauer algebras, generalising our previous construction for two matrices. We will compute multi-point functions of the basis with the exact N-dependence. In particular we study three-point functions of a class of BPS operators, and we find that they are given by a branching rule of the Brauer algebra. The three-point functions take a factorised form if representations on the operators satisfy a relation.

Gribov horizon and spontaneous BRST symmetry breaking

An equivalent formulation of the Gribov--Zwanziger theory accounting for the gauge fixing ambiguity in the Landau gauge is presented. The resulting action is constrained by a Slavnov-Taylor identity stemming from a nilpotent exact Becchi-Rouet-Stora-Tyutin (BRST) invariance which is spontaneously broken due to the presence of the Gribov horizon. This spontaneous symmetry breaking can be described in a purely algebraic way through the introduction of a pair of auxiliary fields which give rise to a set of linearly broken Ward identities. The Goldstone sector turns out to be decoupled. The underlying exact nilpotent BRST invariance allows us to employ BRST cohomology tools within the Gribov horizon to identify renormalizable extensions of gauge invariant operators. Using a simple toy model and appropriate Dirac bracket quantization, we discuss the time evolution invariance of the operator cohomology. We further comment on the unitarity issue in a confining theory, and stress that BRST cohomology alone is not sufficient to ensure unitarity, a fact that, although well known, is frequently ignored.

The spin of holographic electrons at nonzero density and temperature

We study the Green's function of a gauge invariant fermionic operator in a strongly coupled field theory at nonzero temperature and density using a dual gravity description. The gravity model contains a charged black hole in four dimensional anti-de Sitter space and probe charged fermions. In particular, we consider the effects of the spin of these probe fermions on the properties of the Green's function. There exists a spin-orbit coupling between the spin of an electron and the electric field of a Reissner-Nordstrom black hole. On the field theory side, this coupling leads to a Rashba like dispersion relation. We also study the effects of spin on the damping term in the dispersion relation by considering how the spin affects the placement of the fermionic quasinormal modes in the complex frequency plane in a WKB limit. An appendix contains some exact solutions of the Dirac equation in terms of Heun polynomials.

OPE in planar QCD from integrability

We consider the operator product expansion of local gauge-invariant singletrace operators composed of self-dual components of the field strength tensor in planar QCD. Using the integrability of the 1-loop dilatation operator, we obtain a determinant expression for certain tree-level structure constants.

On correlation functions of Wilson loops, local and non-local operators

We discuss and extend recent conjectures relating partial null limits of correlation functions of local gauge invariant operators and the expectation value of null polygonal Wilson loops and local gauge invariant operators. We point out that a particular partial null limit provides a strategy for the calculation of the anomalous dimension of short twist-two operators at weak and strong coupling.

Gauge-invariant correlation functions in light-cone superspace

We initiate a study of correlation functions of gauge-invariant operators in $ \mathcal{N} = 4 $ super Yang-Mills theory using the light-cone superspace formalism. Our primary aim is to develop efficient methods to compute perturbative corrections to correlation functions. This analysis also allows us to examine potential subtleties which may arise when calculating off-shell quantities in light-cone gauge. We comment on the intriguing possibility that the manifest $ \mathcal{N} = 4 $ supersymmetry in this approach may allow for a compact description of entire multiplets and their correlation functions.

Massive photons and Lorentz violation

All quadratic translation- and gauge-invariant photon operators for Lorentz breakdown are included into the Stueckelberg Lagrangian for massive photons in a generalized \xi-gauge. The corresponding dispersion relation and tree-level propagator are determined exactly, and some leading-order results are derived. The question of how to include such Lorentz-violating effects into a perturbative quantum-field expansion is addressed. Applications of these results within Lorentz-breaking quantum field theories include the regularization of infrared divergences as well as the free propagation of massive vector bosons.