Four-dimensional noncommutative deformations of U(1) gauge theory and L∞ bootstrap.

We construct a family of four-dimensional noncommutative deformations of U(1) gauge theory following a general scheme, recently proposed in JHEP 08 (2020) 041 for a class of coordinate-dependent noncommutative algebras. This class includes the $$ \mathfrak{su} $$ su (2), the $$ \mathfrak{su} $$ su (1, 1) and the angular (or λ-Minkowski) noncommutative structures. We find that the presence of a fourth, commutative coordinate x0 leads to substantial novelties in the expression for the deformed field strength with respect to the corresponding three-dimensional case. The constructed field theoretical models are Poisson gauge theories, which correspond to the semi-classical limit of fully noncommutative gauge theories. Our expressions for the deformed gauge transformations, the deformed field strength and the deformed classical action exhibit flat commutative limits and they are exact in the sense that all orders in the deformation parameter are present. We review the connection of the formalism with the L∞ bootstrap and with symplectic embeddings, and derive the L∞-algebra, which underlies our model.

Maximally supersymmetric RG flows in 4D and integrability

We revisit the leading irrelevant deformation of $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory that preserves sixteen supercharges. We consider the deformed theory on S3× ℝ. We are able to write a closed form expression of the classical action thanks to a formalism that realizes eight supercharges off shell. We then investigate integrability of the spectral problem, by studying the spin-chain Hamiltonian in planar perturbation theory. While there are some structural indications that a suitably defined deformation might preserve integrability, we are unable to settle this question by our two-loop calculation; indeed up to this order we recover the integrable Hamiltonian of undeformed $$ \mathcal{N} $$ N = 4 SYM due to accidental symmetry enhancement. We also comment on the holographic interpretation of the theory.

The hidden fluxes, that control the fluctuations of scalar fields

The fluctuations of scalar fields, that are invariant under rotations of the worldvolume, in Euclidian signature, can be described by a system of Langevin equations. These equations can be understood as defining a change of variables in the functional integral for the noise, with which the physical degrees of freedom are in equilibrium. The absolute value of the Jacobian of this change of variables therefore repackages the fluctuations. This provides a new way of relating the number and properties of scalar fields with the consistent and complete description of their fluctuations and is another way of understanding the relevance of supersymmetry, which, in this way, determines the minimal number of real scalar fields (e.g. two in two dimensions, four in three dimensions and eight in four dimensions), in order for the system to be consistently closed. The classical action of the scalar fields, obtained in this way, contains a surface term and a remainder, in addition to the canonical kinetic and potential terms. The surface term describes possible flux contributions in the presence of boundaries, while the remainder describes additional interactions, that can’t be absorbed in a redefinition of the canonical terms. It is, however, through its combination with the surface term that the noise fields can be recovered, in all cases. However their identities can be subject to anomalies. What is of particular, practical, interest is the identification of the noise fields, as functions of the scalars, whose correlation functions are Gaussian. This implies new identities, between the scalars, that can be probed in real, or computer, experiments.

Wilson loops in $$ \mathcal{N} $$ = 4 SO(N) SYM and D-branes in AdS5 × ℝℙ5

We study the half-BPS circular Wilson loop in $$ \mathcal{N} $$ N = 4 super Yang-Mills with orthogonal gauge group. By supersymmetric localization, its expectation value can be computed exactly from a matrix integral over the Lie algebra of SO(N). We focus on the large N limit and present some simple quantitative tests of the duality with type IIB string theory in AdS5× ℝℙ5. In particular, we show that the strong coupling limit of the expectation value of the Wilson loop in the spinor representation of the gauge group precisely matches the classical action of the dual string theory object, which is expected to be a D5-brane wrapping a ℝℙ4 subspace of ℝℙ5. We also briefly discuss the large N, large λ limits of the SO(N) Wilson loop in the symmetric/antisymmetric representations and their D3/D5-brane duals. Finally, we use the D5-brane description to extract the leading strong coupling behavior of the “bremsstrahlung function” associated to a spinor probe charge, or equivalently the normalization of the two-point function of the displacement operator on the spinor Wilson loop, and obtain agreement with the localization prediction.

Limiting fluctuations in quantum gravity to diffeomorphisms

Within the background field formalism of quantum gravity, I show that if the quantum fluctuations are limited to diffeomorphic gauge transformations rather than the physical degrees of freedom, as in conventional quantum field theory, all the quantum corrections vanish on shell and the effective action is equivalent to the classical action. In principle, the resulting theory is finite and unitary, and requires no renormalization. I also show that this is the unique parameterization that renders the path integral independent of the on-shell condition for the background field, a form of background independence. Thus, a connection is established between background independence and renormalizability and unitarity.

Frame covariant formalism for fermionic theories

We present a frame- and reparametrisation-invariant formalism for quantum field theories that include fermionic degrees of freedom. We achieve this using methods of field-space covariance and the Vilkovisky–DeWitt (VDW) effective action. We explicitly construct a field-space supermanifold on which the quantum fields act as coordinates. We show how to define field-space tensors on this supermanifold from the classical action that are covariant under field reparametrisations. We then employ these tensors to equip the field-space supermanifold with a metric, thus solving a long-standing problem concerning the proper definition of a metric for fermionic theories. With the metric thus defined, we use well-established field-space techniques to extend the VDW effective action and express any fermionic theory in a frame- and field-reparametrisation-invariant manner.

A new Wilson line-based action for gluodynamics

We perform a canonical transformation of fields that brings the Yang-Mills action in the light-cone gauge to a new classical action, which does not involve any triple-gluon vertices. The lowest order vertex is the four-point MHV vertex. Higher point vertices include the MHV and $$ \overline{\mathrm{MHV}} $$ MHV ¯ vertices, that reduce to the corresponding amplitudes in the on-shell limit. In general, any n-leg vertex has 2 ≤ m ≤ n − 2 negative helicity legs. The canonical transformation of fields can be compactly expressed in terms of path-ordered exponentials of fields and their functional derivative. We apply the new action to compute several tree-level amplitudes, up to 8-point NNMHV amplitude, and find agreement with the standard methods. The absence of triple-gluon vertices results in fewer diagrams required to compute amplitudes, when compared to the CSW method and, obviously, considerably fewer than in the standard Yang-Mills action.

On a gauge-invariant deformation of a classical gauge-invariant theory

We consider a general gauge theory with independent generators and study the problem of gauge-invariant deformation of initial gauge-invariant classical action. The problem is formulated in terms of BV-formalism and is reduced to describing the general solution to the classical master equation. We show that such general solution is determined by two arbitrary generating functions of the initial fields. As a result, we construct in explicit form the deformed action and the deformed gauge generators in terms of above functions. We argue that the deformed theory must in general be non-local. The developed deformation procedure is applied to Abelian vector field theory and we show that it allows to derive non-Abelain Yang-Mills theory. This procedure is also applied to free massless integer higher spin field theory and leads to local cubic interaction vertex for such fields.

CHOPPED-POT SITUATION IN TEACHERS DEVELOPMENT VIA ACTION RESEARCH TECHNIQUES IN CYBER ERA

Chopped-pot (chop pot) is a poker term and a critical opening metaphor for this article. Applied action research steps and these extensions are necessary for practice during a pandemical situation in unstable and challenging teaching at universities in Czechia. Forms of teaching, personal contact and process of monitoring students’ results have changed dynamically. Mass influence of pandemic situation stopped actions at schools and many institutions all over the world. In Czechia, there has been transferred all practical and cognitive (theoretical) subjects to cyberspace. Due to the lack of government information, public fear and low digital literacy level, students have been learning in virtual classes and individual consultations. Many of them have lost contact with their critical practice and opportunities to transfer their knowledge into the school environment. We tried to modify classical action research approaches to new conditions in cyberspace and use it for pre-service and teachers’ innovation from an innovative perspective. In the methodological part, there is research presented from a full semester of gradual teachers’ development. The constructed research tool was tested in virtual conditions and monitored activities and the progress of development in teachers’ self-reflection for their future daily practice. The mixed design of research tools and a combination of the postproduction process of data open scientific feedback for their subjective inquiries in the individual personal development of educational staff in Czechia via action research model.