N=2 String as a Topological Conformal Algebra

We prove that critical and subcritical N=2 string theory gives a realization of an N=2 superfield extension of the topological conformal algebra. The essential observation is the vanishing of the background charge.Comment: 11 page

On Evaluation of Nonplanar Diagrams in Noncommutative Field Theory

This is a technical work about how to evaluate loop integrals appearing in one loop nonplanar (NP) diagrams in noncommutative (NC) field theory. The conventional wisdom says that, barring the ultraviolet/infrared (UV/IR) mixing problem, NP diagrams whose planar counterparts are UV divergent are rendered finite by NC phases that couple the loop momentum to the external NC momentum \rho^{\mu}=\theta^{\mu\nu}p_{\nu}. We show that this is generally not the case. We find that subtleties arise already on Euclidean spacetime. The situation is even worse in Minkowski spacetime due to its indefinite metric. We compare different prescriptions that may be used to evaluate loop integrals in ordinary theory. They are equivalent in the sense that they always yield identical results. However, in NC theory there is no a priori reason that these prescriptions, except for the defining one built in Feynman propagator, are physically justified. Employing them can lead to ambiguous results. For \rho^2>0, the NC phase can worsen the UV property of loop integrals instead of always improving it in high dimensions. We explain how this surprising phenomenon comes about from the indefinite metric. For \rho^2<0, the NC phase improves the UV property and softens the quadratic UV divergence in ordinary theory to a bounded but indefinite UV oscillation. We employ a cut-off method to quantify the new UV non-regular terms. For \rho^2>0, these terms are generally complex and thus also harm unitarity. As the new terms are not available in the Lagrangian, our result casts doubts on previous demonstrations of one loop renormalizability based exclusively upon analysis of planar diagrams, especially in theories with quadratic divergences.Comment: 29 pages, no figs; v2: (1) some clarifying discussions concerning cut-off method are added at the end of subsec 2.2 and in subsec 4.5; (2) typos are fixed and some minor rewordings are made; (3) acknowledgements extended. Version to appear in Nucl. Phys.

Securing the Execution of ML Workflows across the Compute Continua

Cloud computing has become the major computational paradigm for the deployment of all kind of applications, ranging from mobile apps to complex AI algorithms. On the other side, the rapid growth of IoT market has led to the need of processing the data produced by smart devices using their embedded resources. The computing continuum paradigm aims at solving the issues related to the deployment of applications across edge-to-cloud cyber-infrastructures.This work considers in-memory data protection to enhance security over the compute continua and proposes a solution for the development of distributed applications that handles security in a transparent way for the developer. The proposed framework has been evaluated using an ML application that classifies health data using a pre-trained model. The results show that securing in-memory data incurs no additional effort at development time and the overheads introduced by the encryption mechanisms do not compromise the scalability of the application.This work has been supported by the Spanish Government (PID2019-107255GB) and by MCIN/AEI /10.13039/501100011033 (CEX2021- 001148-S), by Generalitat de Catalunya (contract 2021-SGR-00412),and by the European Commission through the Horizon Europe Research and Innovation program under Grant Agreement No.101016577 (AI-SPRINT project).Peer ReviewedPostprint (author's final draft

Comments on Perturbative Dynamics of Non-Commutative Yang-Mills Theory

We study the U(N) non-commutative Yang-Mills theory at the one-loop approximation. We check renormalizability and gauge invariance of the model and calculate the one-loop beta function. The interaction of the SU(N) gauge bosons with the U(1) gauge boson plays an important role in the consistency check. In particular, the SU(N) theory by itself is not consistent. We also find that the theta --> 0 limit of the U(N) theory does not converge to the ordinary SU(N) x U(1) commutative theory, even at the planar limit. Finally, we comment on the UV/IR mixing.Comment: 19 pages, Latex. 4 figures. v2: minor changes, refs. added. To appear in Nucl.Phys.

Perturbative Noncommutative Quantum Gravity

We study perturbative noncommutative quantum gravity by expanding the gravitational field about a fixed classical background. A calculation of the one loop gravitational self-energy graph reveals that only the non-planar graviton loops are damped by oscillating internal momentum dependent factors. The noncommutative quantum gravity perturbation theory is not renormalizable beyond one loop for matter-free gravity and all loops for matter interactions. Comments are made about the nonlocal gravitational interactions produced by the noncommutative spacetime geometry.Comment: 11 pages LaTex. No figures. Changes to text. To be published in Physics Letters

Supergravity Dual of Noncommutative N=1 SYM

We construct the noncommutative deformation of the Maldacena-Nunez supergravity solution. The background describes a bound state of D5-D3 branes wrapping an S^2 inside a Calabi-Yau three-fold, and in the presence of a magnetic B-field. The dual field theory in the IR is a N=1 U(N) SYM theory with spatial noncommutativity. We show that, under certain conditions, the massive Kaluza-Klein states can be decoupled and that UV/IR mixing seems to be visible in our solution. By calculating the quark-antiquark potential via the Wilson loop we show confinement in the IR and strong repulsion at closer distances. We also compute the beta-function and show that it coincides with the recently calculated commutative one.Comment: 24 pages, latex, 4 figures; v2 references added, correction of a sign mistake in the expression of the curvatur

Tree Unitarity and Partial Wave Expansion in Noncommutative Quantum Field Theory

The validity of the tree-unitarity criterion for scattering amplitudes on the noncommutative space-time is considered, as a condition that can be used to shed light on the problem of unitarity violation in noncommutative quantum field theories when time is noncommutative. The unitarity constraints on the partial wave amplitudes in the noncommutative space-time are also derived.Comment: 15 pages, 1 figur

Casimir Effect on the Radius Stabilization of the Noncommutative Torus

We evaluate the one-loop correction to the spectrum of Kaluza-Klein system for the $\phi^3$ model on $R^{1,d}\times (T_\theta^2)^L$, where $1+d$ dimensions are the ordinary flat Minkowski spacetimes and the extra dimensions are the L two-dimensional noncommutative tori with noncommutativity $\theta$. The correction to the Kaluza-Klein mass spectrum is then used to compute the Casimir energy. The results show that when $L>2$ the Casimir energy due to the noncommutativity could give repulsive force to stabilize the extra noncommutative tori in the cases of $d = 4n - 2$, with $n$ a positive integral.Comment: Latex, 11page

On the BRST Operator Structure of the N=2 String

The BRST operator cohomology of $N=2$ $2d$ supergravity coupled to matter is presented. Descent equations for primary superfields of the matter sector are derived. We find one copy of the cohomology at ghost number one, two independent copies at ghost number two, and conjecture that there is a copy at ghost number three. The $N=2$ string has a twisted $N=4$ superconformal symmetry generated by the $N=2$ superstress tensor, the BRST supercurrent, the antighost superfield, and the ghost number supercurrent.Comment: 22 pages, Latex, NSF-ITP-93-17, ITP-SB-93-09, RIP-148-9