Quantum Gauge Research Articles

The Discreet Charm of Higgsino Dark Matter: A Pocket Review

We give a brief review of the current constraints and prospects for detection of higgsino dark matter in low-scale supersymmetry. In the first part we argue, after performing a survey of all potential dark matter particles in the MSSM, that the (nearly) pure higgsino is the only candidate emerging virtually unscathed from the wealth of observational data of recent years. In doing so by virtue of its gauge quantum numbers and electroweak symmetry breaking only, it maintains at the same time a relatively high degree of model-independence. In the second part we properly review the prospects for detection of a higgsino-like neutralino in direct underground dark matter searches, collider searches, and indirect astrophysical signals. We provide estimates for the typical scale of the superpartners and fine tuning in the context of traditional scenarios where the breaking of supersymmetry is mediated at about the scale of Grand Unification and where strong expectations for a timely detection of higgsinos in underground detectors are closely related to the measured 125 GeV mass of the Higgs boson at the LHC.

A path integral based model for stocks and order dynamics

We present a model for the short-term dynamics of financial assets based on an application to finance of quantum gauge theory, developing ideas of Ilinski. We present a numerical algorithm for the computation of the probability distribution of prices and compare the results with APPLE stocks prices and the S&P500 index.

Phase diagram of QCD chaos in linear sigma models and holography

Measuring chaos of QCD-like theories is a challenge for formulating a novel characterization of quantum gauge theories. We define a chaos phase diagram of QCD allowing us to locate chaos in the parameter space of energy of homogeneous meson condensates and the QCD parameters such as pion/quark mass. We draw the chaos phase diagrams obtained in two ways: first, by using a linear sigma model, varying parameters of the potential, and second, by using the D4/D6 holographic QCD, varying the number of colors $N_c$ and the 't Hooft coupling constant $\lambda$. A scaling law drastically simplifies our analyses, and we discovered that the chaos originates in the maximum of the potential, and larger $N_c$ or larger $\lambda$ diminishes the chaos.

Two-loop renormalization of the Faddeev-Popov ghosts in mathcal{N}=1 supersymmetric gauge theories regularized by higher derivatives

For the general renormalizable mathcal{N}=1 supersymmetric gauge theory we investigate renormalization of the Faddeev-Popov ghosts using the higher covariant derivative regularization. First, we find the two-loop anomalous dimension defined in terms of the bare coupling constant in the general ξ-gauge. It is demonstrated that for doing this calculation one should take into account that the quantum gauge superfield is renormalized in a nonlinear way. Next, we obtain the two-loop anomalous dimension of the Faddeev-Popov ghosts defined in terms of the renormalized coupling constant and examine its dependence on the subtraction scheme.

Formula omitted] “Nuclear Physics” with ultracold Gases

An ab initio calculation of nuclear physics from Quantum Chromodynamics (QCD), the fundamental SU(3) gauge theory of the strong interaction, remains an outstanding challenge. Here, we discuss the emergence of key elements of nuclear physics using an SO(3) lattice gauge theory as a toy model for QCD. We show that this model is accessible to state-of-the-art quantum simulation experiments with ultracold atoms in an optical lattice. First, we demonstrate that our model shares characteristic many-body features with QCD, such as the spontaneous breakdown of chiral symmetry, its restoration at finite baryon density, as well as the existence of few-body bound states. Then we show that in the one-dimensional case, the dynamics in the gauge invariant sector can be encoded as a spin S=32 Heisenberg model, i.e., as quantum magnetism, which has a natural realization with bosonic mixtures in optical lattices, and thus sheds light on the connection between non-Abelian gauge theories and quantum magnetism.

New form of the exact NSVZ \u03b2-function: the three-loop verification for terms containing Yukawa couplings

We investigate a recently proposed new form of the exact NSVZ β-function, which relates the β-function to the anomalous dimensions of the quantum gauge superfield, of the Faddeev-Popov ghosts, and of the chiral matter superfields. Namely, for the general renormalizable mathcal{N} = 1 supersymmetric gauge theory, regularized by higher covariant derivatives, the sum of all three-loop contributions to the β-function containing the Yukawa couplings is compared with the corresponding two-loop contributions to the anomalous dimensions of the quantum superfields. It is demonstrated that for the considered terms both new and original forms of the NSVZ relation are valid independently of the subtraction scheme if the renormalization group functions are defined in terms of the bare couplings. This result is obtained from the equality relating the loop integrals, which, in turn, follows from the factorization of the integrals for the β-function into integrals of double total derivatives. For the renormalization group functions defined in terms of the renormalized couplings we verify that the NSVZ scheme is obtained with the higher covariant derivative regularization supplemented by the subtraction scheme in which only powers of ln Λ/μ are included into the renormalization constants.

Solvable spectral problems from 2d CFT and = 2 gauge theories

The so-called 2d/4d correspondences connect two-dimensional conformal field theory (2d CFT), = 2 supersymmetric gauge theories and quantum integrable systems. The latter in the simplest case of the SU(2) gauge group are nothing but the quantum-mechanical systems. In the present article we summarize our recent results and list open problems concerning an application of the aforementioned dualities in the studies of spectral problems for some Schrödinger operators with Mathieu–type periodic, periodic PT–symmetric and (Heun’s) elliptic potentials.

Quantum properties of supersymmetric theories regularized by higher covariant derivatives

We investigate quantum corrections in = 1 non-Abelian supersymmetric gauge theories, regularized by higher covariant derivatives. In particular, by the help of the Slavnov–Taylor identities we prove that the vertices with two ghost legs and one leg of the quantum gauge superfield are finite in all orders. This non-renormalization theorem is confirmed by an explicit one-loop calculation. By the help of this theorem we rewrite the exact NSVZ β-function in the form of the relation between the β-function and the anomalous dimensions of the matter superfields, of the quantum gauge superfield, and of the Faddeev–Popov ghosts. Such a relation has simple qualitative interpretation and allows suggesting a prescription producing the NSVZ scheme in all loops for the theories regularized by higher derivatives. This prescription is verified by the explicit three-loop calculation for the terms quartic in the Yukawa couplings.

Gaugeon formalism for the second-rank antisymmetric tensor gauge fields

We present a BRST symmetric gaugeon formalism for the two-form gauge fields. A set of vector gaugeon fields is introduced as a quantum gauge freedom. One of the gaugeon fields satisfies a higher derivative field equation; this property is necessary to change the gauge-fixing parameter of the two-form gauge field. A naive Lagrangian for the vector gaugeon fields is itself invariant under a gauge transformation for the vector gaugeon field. The Lagrangian of our theory includes the gauge-fixing terms for the gaugeon fields and corresponding Faddeev--Popov ghosts terms.

Asymptotic symmetries, holography and topological hair

Asymptotic symmetries of AdS4 quantum gravity and gauge theory are derived by coupling the holographically dual CFT3 to Chern-Simons gauge theory and 3D gravity in a “probe” (large-level) limit. Despite the fact that the three-dimensional AdS4 boundary as a whole is consistent with only finite-dimensional asymptotic symmetries, given by AdS isometries, infinite-dimensional symmetries are shown to arise in circumstances where one is restricted to boundary subspaces with effectively two-dimensional geometry. A canonical example of such a restriction occurs within the 4D subregion described by a Wheeler-DeWitt wavefunctional of AdS4 quantum gravity. An AdS4 analog of Minkowski “super-rotation” asymptotic symmetry is probed by 3D Einstein gravity, yielding CFT2 structure (in a large central charge limit), via AdS3 foliation of AdS4 and the AdS3/CFT2 correspondence. The maximal asymptotic symmetry is however probed by 3D conformal gravity. Both 3D gravities have Chern-Simons formulation, manifesting their topological character. Chern-Simons structure is also shown to be emergent in the Poincare patch of AdS4, as soft/boundary limits of 4D gauge theory, rather than “put in by hand” as an external probe. This results in a finite effective Chern-Simons level. Several of the considerations of asymptotic symmetry structure are found to be simpler for AdS4 than for Mink4, such as non-zero 4D particle masses, 4D non-perturbative “hard” effects, and consistency with unitarity. The last of these in particular is greatly simplified because in some set-ups the time dimension is explicitly shared by each level of description: Lorentzian AdS4, CFT3 and CFT2. Relatedly, the CFT2 structure clarifies the sense in which the infinite asymptotic charges constitute a useful form of “hair” for black holes and other complex 4D states. An AdS4 analog of Minkowski “memory” effects is derived, but with late-time memory of earlier events being replaced by (holographic) “shadow” effects. Lessons from AdS4 provide hints for better understanding Minkowski asymptotic symmetries, the 3D structure of its soft limits, and Minkowski holography.

Supersymmetry, quantum corrections, and the higher derivative regularization

We investigate the structure of quantum corrections in N = 1 supersymmetric theories using the higher covariant derivative method for regularization. In particular, we discuss the non-renormalization theorem for the triple gauge-ghost vertices and its connection with the exact NSVZ β-function. Namely, using the finiteness of the triple gauge-ghost vertices we rewrite the NSVZ equation in a form of a relation between the β-function and the anomalous dimensions of the quantum gauge superfield, of the Faddeev-Popov ghosts, and of the matter superfields. We argue that it is this form that follows from the perturbative calculations, and give a simple prescription how to construct the NSVZ scheme in the non-Abelian case. These statements are confirmed by an explicit calculation of the three-loop contributions to the β-function containing Yukawa couplings. Moreover, we calculate the two-loop anomalous dimension of the ghost superfields and demonstrate that for doing this calculation it is very important that the quantum gauge superfield is renormalized non-linearly.

Integral Lattice Models from Gauge Theory

These notes provide an introduction to recent work by Kevin Costello in which integrable lattice models of classical statistical mechanics in two dimensions are understood in terms of quantum gauge theory in four dimensions. This construction will be compared to the more familiar relationship between quantum knot invariants in three dimensions and Chern-Simons gauge theory. (Based on a Whittaker Colloquium at the University of Edinburgh and a lecture at Strings 2016 in Beijing.)

Mini-Workshop: New Interactions between Homotopical Algebra and Quantum Field Theory

Recent developments in quantum field theory strongly call for techniques from homotopical algebra to develop the mathematical foundations of quantum gauge theories. This mini-workshop brought together experts working at the interface between topological field theory, quantum field theory and homotopical algebra with the goal of triggering major advances towards understanding quantum gauge theory. This was achieved via a fruitful exchange of ideas and technologies across different research communities and encouraging a comparison between recent approaches to homotopical quantum field theory.

Quantum gauge freedom in the Lorentz violating background

In this paper, we will study the Lorentz symmetry breaking down to its subgroup. A two-form gauge theory is investigated in the Lorentz violating background and it will be shown that this symmetry violation affects the structure of this gauge theory. In particular, we will study the gaugeon formalism and FFBRST for such a theory in this broken spacetime. In addition to Kugo-Ojima type condition, a thorough evaluation of quantum gauge freedom and gaugeon modes is carried out. We will explicitly demonstrate that in Lorentz broken spacetime, our reducible gauge theory fully depicts the physical aspects of gaugeon fields.

Bessel-like functional distributions in brain average evoked potentials.

Average evoked potential data recorded as impulse responses of brains to electric shocks show Bessel-like functional distributions which we analyze in terms of couples of damped/amplified oscillators. This reproduces results obtained in terms of ordinary differential equations (Freeman K-sets) and offers the possibility of a direct connection with the dissipative model of brain in the quantum gauge field theory paradigm. We study the control mechanism by fine tuning the model parameters and the brain property of discriminating between two similar behaviors or perceptions. We suggest that a similar control mechanism may be useful in security communication protocols. Finally, brain activity and mental activity is considered in the light of our results.

New form of the NSVZ relation at the two-loop level

Recently the exact NSVZ β-function was rewritten in the form of a relation between the β-function and the anomalous dimensions of the quantum gauge superfield, of the Faddeev–Popov ghosts, and of the matter superfields. It was also suggested that this form of the NSVZ equation follows from an underlying equation relating two-point Green functions of the theory. Here we demonstrate that this relation is satisfied at the two-loop level for the non-Abelian N=1 supersymmetric gauge theories in the case of using the simplest (BRST non-invariant) version of the higher covariant derivative regularization. Consequently, the integrals giving the two-loop β-function can be reduced to the one-loop integrals giving the anomalous dimensions of the quantum gauge superfield, of the Faddeev–Popov ghosts, and of the matter superfields.

Perturbative Quantum Gauge Theories on Manifolds with Boundary

This paper introduces a general perturbative quantization scheme for gauge theories on manifolds with boundary, compatible with cutting and gluing, in the cohomological symplectic (BV-BFV) formalism. Explicit examples, like abelian BF theory and its perturbations, including nontopological ones, are presented.

Lorentz-violating Yang\u2013Mills theory: discussing the Chern\u2013Simons-like term generation

We analyze the Chern–Simons-like term generation in the CPT-odd Lorentz-violating Yang–Mills theory interacting with fermions. Moreover, we study the anomalies of this model as well as its quantum stability. The whole analysis is performed within the algebraic renormalization theory, which is independent of the renormalization scheme. In addition, all results are valid to all orders in perturbation theory. We find that the Chern–Simons-like term is not generated by radiative corrections, just like its Abelian version. Additionally, the model is also free of gauge anomalies and quantum stable.

One-loop polarization operator of the quantum gauge superfield for 𝒩 = 1 SYM regularized by higher derivatives

We consider the general [Formula: see text] supersymmetric gauge theory with matter, regularized by higher covariant derivatives without breaking the BRST invariance, in the massless limit. In the [Formula: see text]-gauge we obtain the (unrenormalized) expression for the two-point Green function of the quantum gauge superfield in the one-loop approximation as a sum of integrals over the loop momentum. The result is presented as a sum of three parts: the first one corresponds to the pure supersymmetric Yang–Mills theory in the Feynman gauge, the second one contains all gauge-dependent terms, and the third one is the contribution of diagrams with a matter loop. For the Feynman gauge and a special choice of the higher derivative regulator in the gauge fixing term, we analytically calculate these integrals in the limit [Formula: see text]. In particular, in addition to the leading logarithmically divergent terms, which are determined by integrals of double total derivatives, we also find the finite constants.

Surprises from complete vector portal theories: New insights into the dark sector and its interplay with Higgs physics

We study UV complete theories where the Standard Model (SM) gauge group is extended with a new abelian $U(1)$, and the field content is augmented by an arbitrary number of scalar and fermion SM singlets, potentially including dark matter (DM) candidates. Considerations such as classical and quantum gauge invariance of the full theory and S-matrix unitarity, not applicable within a simplified model approach, are shown to have significant phenomenological consequences. The lack of gauge anomalies leads to compact relations among the $U(1)$ fermion charges, and puts a lower bound on the number of dark fermions. Contrary to naive expectations, the DM annihilation to Zh is found to be p-wave suppressed, as hinted by perturbative unitarity of S-matrix, with dramatic implications for DM thermal relic density and indirect searches. Within this framework, the interplay between dark matter, new vector boson and Higgs physics is rather natural and generic.