Superconformal duality-invariant models and $$ \mathcal{N} $$ = 4 SYM effective action

We present $$ \mathcal{N} $$ N = 2 superconformal U(1) duality-invariant models for an Abelian vector multiplet coupled to conformal supergravity. In a Minkowski background, such a nonlinear theory is expected to describe (the planar part of) the low-energy effective action for the $$ \mathcal{N} $$ N = 4 SU(N) super-Yang-Mills (SYM) theory on its Coulomb branch where (i) the gauge group SU(N) is spontaneously broken to SU(N − 1) × U(1); and (ii) the dynamics is captured by a single $$ \mathcal{N} $$ N = 2 vector multiplet associated with the U(1) factor of the unbroken group. Additionally, a local U(1) duality-invariant action generating the $$ \mathcal{N} $$ N = 2 super-Weyl anomaly is proposed. By providing a new derivation of the recently constructed U(1) duality-invariant $$ \mathcal{N} $$ N = 1 superconformal electrodynamics, we introduce its SL(2, ℝ) duality-invariant coupling to the dilaton-axion multiplet.

Closed string deformations in open string field theory. Part II. Superstring

This is the second paper of a series of three. We construct effective open-closed superstring couplings by classically integrating out massive fields from open superstring field theories coupled to an elementary gauge invariant tadpole proportional to an on-shell closed string state in both large and small Hilbert spaces, in the NS sector. This source term is well known in the WZW formulation and by explicitly performing a novel large Hilbert space perturbation theory we are able to characterize the first orders of the vacuum shift solution, its obstructions and the non-trivial open-closed effective couplings in closed form. With the aim of getting all order results, we also construct a new observable in the A∞ theory in the small Hilbert space which correctly provides a gauge invariant coupling to physical closed strings and which descends from the WZW open-closed coupling upon partial gauge fixing and field redefinition. Armed with this new A∞ observable we use tensor co-algebra techniques to efficiently package the whole perturbation theory necessary for computing the effective action and we give all order results for the open-closed effective couplings in the small Hilbert space.

On the Lagrangian formulation of the double copy to cubic order

We investigate the Lagrangian formulation of the double-copy correspondence between gauge theories and gravity, up to the cubic order. Building on the definition of the double-copy field as a convolution of two vectors, we obtain free gravitational Lagrangians as products of two Yang-Mills Lagrangians, in a form amenable to be easily extended to the massive case. We discuss the origin of these results from tensionless strings and show the existence of gauge fixings that mix the two spin-one sectors and lead to an alternative, especially simple, version of the free Lagrangian. We then construct cubic vertices for the full double-copy multiplet, comprising a graviton, a two-form and a scalar particle, by means of the Noether procedure. Both at the free and at the cubic level the result gets uniquely fixed only upon imposing, on top of gauge invariance, a left-right Lorentz symmetry ruling contraction of indices among double-copy fields. Whereas the outcome nicely matches the cubic interactions of $$ \mathcal{N} $$ N = 0 supergravity, including the gauge-invariant coupling between the scalar particle and the two-form, such a twofold Lorentz symmetry seems to conflict with the perturbative reconstruction of spacetime geometry.

Coupling to Variant Information: an Ecological Account of Comparative Mental Imagery Generation

Action-based theories of cognition place primary emphasis upon the role that agent-environment coupling plays in the emergence of psychological states. Prima facie, mental imagery seems to present a problem for some of these theories because it is understood to be stimulus-absent and thus thought to be decoupled from the environment. However, mental imagery is much more multifaceted than this “naïve” view suggests. Focusing on a particular kind of imagery, comparative mental imagery generation, this paper demonstrates that although such imagery is stimulus-absent, it is also stimulus-sensitive. Exhibiting stimulus-sensitivity is sufficient for a process to qualify as coupled to the environment. The notion of variant coupling is explicated as the coupling of a cognizer’s perceptual system to variant environmental information. By demarcating the categories of stimulus-absent and stimulus-sensitive cognition, and variant and invariant coupling, this paper expands the conceptual apparatus of action-based theories, suggesting not only a way to address the problem that comparative mental imagery generation presents, but perhaps a way to account for other forms of imagery too.

Nilpotent charges in an interacting gauge theory and an 𝒩 = 2 SUSY quantum mechanical model: (Anti-)chiral superfield approach

We exploit the power and potential of the (anti-)chiral superfield approach (ACSA) to Becchi–Rouet–Stora–Tyutin (BRST) formalism to derive the nilpotent (anti-)BRST symmetry transformations for any arbitrary [Formula: see text]-dimensional interacting non-Abelian 1-form gauge theory where there is an [Formula: see text] gauge invariant coupling between the gauge field and the Dirac fields. We derive the conserved and nilpotent (anti-)BRST charges and establish their nilpotency and absolute anticommutativity properties within the framework of ACSA to BRST formalism. The clinching proof of the absolute anticommutativity property of the conserved and nilpotent (anti-)BRST charges is a novel result in view of the fact that we consider, in our endeavor, only the (anti-)chiral super expansions of the superfields that are defined on the [Formula: see text]-dimensional super-submanifolds of the general [Formula: see text]-dimensional supermanifold on which our [Formula: see text]-dimensional ordinary interacting non-Abelian 1-form gauge theory is generalized. To corroborate the novelty of the above result, we apply the ACSA to an [Formula: see text] supersymmetric (SUSY) quantum mechanical (QM) model of a harmonic oscillator and show that the nilpotent and conserved [Formula: see text] supercharges of this system do not absolutely anticommute.

BIOLOGICALLY INSPIRED FILTERS UTILIZING SPECTRAL PROPERTIES OF TOEPLITZ-BLOCK-TOEPLITZ MATRICES

The construction of filters arising from linear neural networks with feed-backward excitatory-inhibitory connections is presented. Spatially invariant coupling between neurons and the distribution of neuron-receptor units in the form of a uniform square grid yield the TBT (Toeplitz-Block-Toeplitz) connection matrix. Utilizing the relationship between spectral properties of such matrices and their generating functions, the method for construction of recurrent linear networks is addressed. By appropriately bounding the generating function, the connection matrix eigenvalues are kept in the desired range allowing for large matrix inverse to be approximated by a convergent power series. Instead of matrix inversion, the single pass convolution with the filter obtained from the network connection weights is applied when solving the network. For the case of inter-neuron coupling in the form of a function that is expandable in a Fourier series in polar angle, the network response filter is shown to be steerable.

High-order corrections of neutron–neutron scattering cross-section by renormalized hybrid loop-chain propagator in isospin space

Bottomed on isospin-SU(2) invariant coupling model which describes the strong interaction between pion and nucleon–antinucleon, for the first time the differential cross-section (DCS) of neutron–neutron scattering with renormalized infinite high-order hybrid loop-chain propagators is "strictly" calculated. DCSs between cases of the hybrid loop-chain propagator (HLCP) and the tree propagator are compared, and it shows that the radiative corrections we obtained are mainly less than 0.9 in typical range of parameters. These results may indicate that the utilization of HLCP underlying the effective way towards the enhanced precision would be considerable. The outcomes might contribute to studies on the nucleon collisions and also possible issues of some phenomena in particle astrophysics.

Invariant coupling of determinantal measures on sofic groups

To any positive contraction $Q$ on $\ell ^{2}(W)$, there is associated a determinantal probability measure $\mathbf{P}^{Q}$ on $2^{W}$, where $W$ is a denumerable set. Let ${\rm\Gamma}$ be a countable sofic finitely generated group and $G=({\rm\Gamma},\mathsf{E})$ be a Cayley graph of ${\rm\Gamma}$. We show that if $Q_{1}$ and $Q_{2}$ are two ${\rm\Gamma}$-equivariant positive contractions on $\ell ^{2}({\rm\Gamma})$ or on $\ell ^{2}(\mathsf{E})$ with $Q_{1}\leq Q_{2}$, then there exists a ${\rm\Gamma}$-invariant monotone coupling of the corresponding determinantal probability measures witnessing the stochastic domination $\mathbf{P}^{Q_{1}}\preccurlyeq \mathbf{P}^{Q_{2}}$. In particular, this applies to the wired and free uniform spanning forests, which was known before only when ${\rm\Gamma}$ is residually amenable. In the case of spanning forests, we also give a second more explicit proof, which has the advantage of showing an explicit way to create the free uniform spanning forest as a limit over a sofic approximation. Another consequence of our main result is to prove that all determinantal probability measures $\mathbf{P}^{Q}$ as above are $\bar{d}$-limits of finitely dependent processes. Thus, when ${\rm\Gamma}$ is amenable, $\mathbf{P}^{Q}$ is isomorphic to a Bernoulli shift, which was known before only when ${\rm\Gamma}$ is abelian. We also prove analogous results for sofic unimodular random rooted graphs.