arXiv subjects

F. Ruiz Ruiz

Publications and source records attributed to F. Ruiz Ruiz.

At least 19 recordsLinked to original sources

arXiv2016

Perturbative quantization of Yang-Mills theory with classical double as gauge algebra

Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary.

hep-th↗

arXiv2015

Yang-Mills theory for semidirect products ${\rm G}\ltimes\mathfrak{g}^*$ and its instantons

Yang-Mills theory with a symmetry algebra that is the semidirect product $\mathfrak{h}\ltimes\mathfrak{h}^*$ defined by the coadjoint action of a Lie algebra $\mathfrak{h}$ on its dual $\mathfrak{h}^*$ is studied. The gauge group is the semidirect product ${\rm G}_{\mathfrak{h}}\ltimes{\mathfrak{h}^*}$, a noncompact group given by the coadjoint action on $\mathfrak{h}^*$ of the Lie group ${\rm G}_{\mathfrak{h}}$ of $\mathfrak{h}$. For $\mathfrak{h}$ simple, a method to construct the self-antiself dual instantons of the theory and their gauge non\-equivalent deformations is presented. Every ${\rm G}_{\mathfrak{h}}\ltimes{\mathfrak{h}^*}$ instanton has an embedded ${\rm G}_{\mathfrak{h}}$ instanton with the same instanton charge, in terms of which the construction is realized. As an example,$\mathfrak{h}=\mathfrak{s}\mathfrak{u}(2)$ and instanton charge one is considered. The gauge group is in this case $SU(2)\ltimes{\bf R}^3$. Explicit expressions for the selfdual connection, the zero modes and the metric and complex structures of the moduli space are given.

hep-th↗

arXiv2011

Geometric construction of D-branes in WZW models

The geometric description of D-branes in WZW models is pushed forward. Our starting point is a gluing condition\, $J_{+}=FJ_-$ that matches the model's chiral currents at the worldsheet boundary through a linear map $F$ acting on the WZW Lie algebra. The equivalence of boundary and gluing conditions of this type is studied in detail. The analysis involves a thorough discussion of Frobenius integrability, shows that $F$ must be an isometry, and applies to both metrically degenerate and nondegenerate D-branes. The isometry $F$ need not be a Lie algebra automorphism nor constantly defined over the brane. This approach, when applied to isometries of the form $F=R$ with $R$ a constant Lie algebra automorphism, validates metrically degenerate $R$-twined conjugacy classes as D-branes. It also shows that no D-branes exist in semisimple WZW models for constant\, $F=-R$.

hep-th↗

arXiv2011

D-branes with Lorentzian signature in the Nappi-Witten model

Lorentzian signature D-branes of all dimensions for the Nappi-Witten string are constructed. This is done by rewriting the gluing condition $J_+=FJ_-$ for the model chiral currents on the brane as a well posed first order differential problem and by solving it for Lie algebra isometries $F$ other than Lie algebra automorphisms. By construction, these D-branes are not twined conjugacy classes. Metrically degenerate D-branes are also obtained.

hep-th↗

arXiv2008

Seiberg--Witten maps for $\boldsymbol{SO(1,3)}$ gauge invariance and deformations of gravity

A family of diffeomorphism-invariant Seiberg--Witten deformations of gravity is constructed. In a first step Seiberg--Witten maps for an SO(1,3) gauge symmetry are obtained for constant deformation parameters. This includes maps for the vierbein, the spin connection and the Einstein--Hilbert Lagrangian. In a second step the vierbein postulate is imposed in normal coordinates and the deformation parameters are identified with the components $θ^{μν}(x)$ of a covariantly constant bivector. This procedure gives for the classical action a power series in the bivector components which by construction is diffeomorphism-invariant. Explicit contributions up to second order are obtained. For completeness a cosmological constant term is included in the analysis. Covariant constancy of $ θ^{μν}(x) $, together with the field equations, imply that, up to second order, only four-dimensional metrics which are direct sums of two two-dimensional metrics are admissible, the two-dimensional curvatures being expressed in terms of $θ^{μν}$. These four-dimensional metrics can be viewed as a family of deformed emergent gravities.

hep-th↗

arXiv2008

Quantization of the open string on plane-wave limits of dS_n x S^n and non-commutativity outside branes

The open string on the plane-wave limit of $dS_n\times S^n $ with constant $B_2$ and dilaton background fields is canonically quantized. This entails solving the classical equations of motion for the string, computing the symplectic form, and defining from its inverse the canonical commutation relations. Canonical quantization is proved to be perfectly suited for this task, since the symplectic form is unambiguously defined and non-singular. The string position and the string momentum operators are shown to satisfy equal-time canonical commutation relations. Noticeably the string position operators define non-commutative spaces for all values of the string world-sheet parameter $\sig$, thus extending non-commutativity outside the branes on which the string endpoints may be assumed to move. The Minkowski spacetime limit is smooth and reproduces the results in the literature, in particular non-commutativity gets confined to the endpoints.

hep-th↗

arXiv2006

Noncommutative Einstein-Maxwell pp-waves

The field equations coupling a Seiberg-Witten electromagnetic field to noncommutative gravity, as described by a formal power series in the noncommutativity parameters $θ^{αβ}$, is investigated. A large family of solutions, up to order one in $θ^{αβ}$, describing Einstein-Maxwell null pp-waves is obtained. The order-one contributions can be viewed as providing noncommutative corrections to pp-waves. In our solutions, noncommutativity enters the spacetime metric through a conformal factor and is responsible for dilating/contracting the separation between points in the same null surface. The noncommutative corrections to the electromagnetic waves, while preserving the wave null character, include constant polarization, higher harmonic generation and inhomogeneous susceptibility. As compared to pure noncommutative gravity, the novelty is that nonzero corrections to the metric already occur at order one in $θ^{αβ}$.

hep-th↗

arXiv2006

Noncommutative spacetime symmetries: Twist versus covariance

We prove that the Moyal product is covariant under linear affine spacetime transformations. From the covariance law, by introducing an $(x,Θ)$-space where the spacetime coordinates and the noncommutativity matrix components are on the same footing, we obtain a noncommutative representation of the affine algebra, its generators being differential operators in $(x,Θ)$-space. As a particular case, the Weyl Lie algebra is studied and known results for Weyl invariant noncommutative field theories are rederived in a nutshell. We also show that this covariance cannot be extended to spacetime transformations generated by differential operators whose coefficients are polynomials of order larger than one. We compare our approach with the twist-deformed enveloping algebra description of spacetime transformations.

hep-th↗

arXiv2005

Position-dependent noncommutative products: classical construction and field theory

We look in Euclidean $R^4$ for associative star products realizing the commutation relation $[x^μ,x^ν]=iΘ^{μν}(x)$, where the noncommutativity parameters $Θ^{μν}$ depend on the position coordinates $x$. We do this by adopting Rieffel's deformation theory (originally formulated for constant $Θ$ and which includes the Moyal product as a particular case) and find that, for a topology $R^2 \times R^2$, there is only one class of such products which are associative. It corresponds to a noncommutativity matrix whose canonical form has components $Θ^{12}=-Θ^{21}=0$ and $Θ^{34}=-Θ^{43}= θ(x^1,x^2)$, with $þ(x^1,x^2)$ an arbitrary positive smooth bounded function. In Minkowski space-time, this describes a position-dependent space-like or magnetic noncommutativity. We show how to generalize our construction to $n\geq 3$ arbitrary dimensions and use it to find traveling noncommutative lumps generalizing noncommutative solitons discussed in the literature. Next we consider Euclidean $λϕ^4$ field theory on such a noncommutative background. Using a zeta-like regulator, the covariant perturbation method and working in configuration space, we explicitly compute the UV singularities. We find that, while the two-point UV divergences are non-local, the four-point UV divergences are local, in accordance with recent results for constant $Θ$.

hep-th↗

arXiv2005

Trouble with space-like noncommutative field theory

It is argued that the one-loop effective action for a space-like noncommutative scalar field theory does not exist. This indicates that such theories are not renormalizable already at one loop order and suggests supersymmetrization and reinvestigating other types of noncommutativity.

hep-th↗

arXiv2003

Anomaly freedom in Seiberg-Witten noncommutative gauge theories

We show that noncommutative gauge theories with arbitrary compact gauge group defined by means of the Seiberg-Witten map have the same one-loop anomalies as their commutative counterparts. This is done in two steps. By explicitly calculating the $ε^{\m_1\m_2\m_3\m_4}$ part of the renormalized effective action, we first find the would-be one-loop anomaly of the theory to all orders in the noncommutativity parameter $θ^{\m\n}$. And secondly we isolate in the would-be anomaly radiative corrections which are not BRS trivial. This gives as the only true anomaly occurring in the theory the standard Bardeen anomaly of commutative spacetime, which is set to zero by the usual anomaly cancellation condition.

hep-th↗

arXiv2002

UV/IR mixing and the Goldstone theorem in noncommutative field theory

Noncommutative IR singularities and UV/IR mixing in relation with the Goldstone theorem for complex scalar field theory are investigated. The classical model has two coupling constants, $λ_1$ and $λ_2$, associated to the two noncommutative extensions $ϕ^*\starϕ\starϕ^*\starϕ$ and $ϕ^*\starϕ^*\starϕ\starϕ$ of the interaction term $|ϕ|^4$ on commutative spacetime. It is shown that the symmetric phase is one-loop renormalizable for all $λ_1$ and $λ_2$ compatible with perturbation theory, whereas the broken phase is proved to exist at one loop only if $λ_2=0$, a condition required by the Ward identities for global U(1) invariance. Explicit expressions for the noncommutative IR singularities in the 1PI Green functions of both phases are given. They show that UV/IR duality does not hold for any of the phases and that the broken phase is free of quadratic noncommutative IR singularities. More remarkably, the pion selfenergy does not have noncommutative IR singularities at all, which proves essential to formulate the Goldstone theorem at one loop for all values of the spacetime noncommutativity parameter $θ$.

hep-th↗

arXiv2001

Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry

It is argued that the quadratic and linear non-commutative IR divergences that occur in U(1) theory on non-commutative Minkowski spacetime for small non-commutativity matrices $θ^{μν}$ are gauge-fixing independent. This implies in particular that the perturbative tachyonic instability produced by the quadratic divergences of this type in the vacuum polarization tensor is not a gauge-fixing artifact. Supersymmetry can be introduced to remove from the renormalized Green functions at one loop, not only the non-logarithmic non-commutative IR divergences, but also all terms proportional to $θ^{μν}p_ν$

hep-th↗

arXiv2000

Paramagnetic dominance, the sign of the beta function and UV/IR mixing in non-commutative U(1)

U(1) gauge theory on non-commutative Minkowski space-time in the Feynman-'t Hooft background gauge is studied. In particular, UV divergences and non-commutative IR divergent contributions to the two, three and four-point functions are explicitly computed at one loop. We show that the negative sign of the beta function results from paramagnetism --producing UV charge anti-screening-- prevailing over diamagnetism --giving rise toUV charge screening. This dominance in the field theory setting corresponds to tachyon magnification dominance in the string theory framework. Our calculations provide an explicit realization of UV/IR mixing and lead to an IR renormalization of the coupling constant, where now paramagnetic contributions produce screening and diamagnetic contributions anti-screening.

hep-th↗

arXiv1998

Drived diffusion of vector fields

A model for the diffusion of vector fields driven by external forces is proposed. Using the renormalization group and the $ε$-expansion, the dynamical critical properties of the model with gaussian noise for dimensions below the critical dimension are investigated and new transport universality classes are obtained.

cond-mat.stat-mech↗

arXiv1997

Supersymmetric Yang-Mills-Chern-Simons theory

We prove that three-dimensional N=1 supersymmetric Yang-Mills-Chern-Simons theory is finite to all loops. This leaves open the possibility that different regularization methods give different finite effective actions. We show that for this model dimensional regularization and regularization by dimensional reduction yield the same effective action.

hep-th↗

arXiv1996

BRS symmetry versus supersymmetry in Yang-Mills-Chern-Simons theory

We prove that three-dimensional $N=1$ supersymmetric Yang-Mills-Chern-Simons theory is finite to all loop orders. In general this leaves open the possibility that different regularization methods lead to different finite effective actions. We show that in this model dimensional regularization and regularization by dimensional reduction yield the same effective action. Consequently, the superfield approach preserves BRS invariance for this model.

hep-th↗

arXiv1995

Unitarity violation in non-abelian Pauli-Villars regularization

We regularize QCD using the combination of higher covariant derivatives and Pauli-Villars determinants proposed by Slavnov. It is known that for pure Yang-Mills theory the Pauli-Villars determinants generate unphysical logarithmic radiative corrections at one loop that modify the beta function. Here we prove that when the gauge fields are coupled to fermions so that one has QCD, these unphysical corrections translate into a violation of unitarity. We provide an understanding of this by seeing that Slavnov's choice for the Pauli-Villars determinants introduces extra propagating degrees of freedom that are responsible for the unitarity breaking. This shows that Slavnov's regularization violates unitarity, hence that it should be rejected.

hep-ph↗