Seiberg-Witten Map Research Articles

Neutral Higgs boson pair production at the linear collider in the noncommutative standard model

We study the Higgs boson pair production at the linear collider in the noncommutative extension of the standard model using the Seiberg-Witten map of this to the first order of the noncommutative parameter ${\ensuremath{\Theta}}_{\ensuremath{\mu}\ensuremath{\nu}}$. Unlike the standard model (where the process is forbidden) here the Higgs boson pair directly interacts with the photon. We find that the pair production cross section can be quite significant for the noncommutative scale $\ensuremath{\Lambda}$ lying in the range 0.5 TeV to 1.0 TeV. Using the experimental (LEP 2, Tevatron, and global electroweak fit) bound on the Higgs mass, we obtain $626\text{ }\text{ }\mathrm{GeV}\ensuremath{\le}\ensuremath{\Lambda}\ensuremath{\le}974\text{ }\text{ }\mathrm{GeV}$.

SEIBERG–WITTEN EQUATIONS FROM FEDOSOV DEFORMATION QUANTIZATION OF ENDOMORPHISM BUNDLE

It is shown how Seiberg–Witten equations can be obtained by means of Fedosov deformation quantization of endomorphism bundle and the corresponding theory of equivalences of star products. In such setting, Seiberg–Witten map can be iteratively computed for arbitrary gauge group up to any given degree with recursive methods of Fedosov construction. Presented approach can be also considered as a generalization of Seiberg–Witten equations to Fedosov type of noncommutativity.

U(2,2)gravity on noncommutative space with symplectic structure

The classical Einstein's gravity can be reformulated from the constrained $U(2,2)$ gauge theory on the ordinary (commutative) four-dimensional spacetime. Here we consider a noncommutative manifold with a symplectic structure and construct a $U(2,2)$ gauge theory on such a manifold by using the covariant coordinate method. Then we use the Seiberg-Witten map to express noncommutative quantities in terms of their commutative counterparts up to the first order in noncommutative parameters. After imposing constraints we obtain a noncommutative gravity theory described by the Lagrangian with up to nonvanishing first-order corrections in noncommutative parameters. This result coincides with our previous one obtained for the noncommutative $SL(2,C)$ gravity.

NON-COMMUTATIVE EINSTEIN EQUATIONS AND SEIBERG–WITTEN MAP

The Seiberg–Witten map is a powerful tool in non-commutative field theory, and it has been recently obtained in the literature for gravity itself, to first order in non-commutativity. This paper, relying upon the pure-gravity form of the action functional considered in Ref. 2, studies the expansion to first order of the non-commutative Einstein equations, and whether the Seiberg–Witten map can lead to a solution of such equations when the underlying classical geometry is Schwarzschild. We find that, if one first obtains the non-commutative field equations by varying the action of Ref. 2 with respect to all non-commutative fields, and then tries to solve these equations by expressing the non-commutative fields in terms of the commutative ones via Seiberg–Witten map, no solution of these equations can be obtained when the commutative background is Schwarzschild.

NONCOMMUTATIVE BTZ BLACK HOLE IN DIFFERENT COORDINATES

We consider noncommutative BTZ black hole solutions in two different coordinate systems, the polar and rectangular coordinates. The analysis is carried out by obtaining noncommutative solutions of U(1, 1) × U(1, 1) Chern-Simons theory on AdS3 in the two coordinate systems via the Seiberg-Witten map. This is based on the noncommutative extension of the equivalence between the classical BTZ solution and the solution of ordinary SU(1, 1) × SU(1, 1) Chern-Simons theory on AdS3. The obtained solutions in these noncommutative coordinate systems become different in the first order of the noncommutativity parameter θ.

NoncommutativeQED+QCDand theβfunction for QED

QED based on $\theta$-unexpanded noncomutative space-time in contrast with the noncommutative QED based on $\theta$-expanded U(1) gauge theory via the Seiberg-Witten map, is one-loop renormalizable. Meanwhile it suffers from asymptotic freedom that is not in agreement with the experiment. We show that QED part of $U_\star(3)\times U_\star(1)$ gauge group as an appropriate gauge group for the noncommutative QED+QCD, is not only one-loop renormalizable but also has a $\beta$ function that can be positive, negative and even zero. In fact the $\beta$ function depends on the mixing parameter $\delta_{13}$ as a free parameter and it will be equal to its counterpart in the ordinary QED for $\delta_{13}=0.367\pi$.

SL(2,C)gravity on noncommutative space with Poisson structure

The Einstein's gravity theory can be formulated as an SL(2,C) gauge theory in terms of spinor notations. In this paper, we consider a noncommutative space with the Poisson structure and construct an SL(2,C) formulation of gravity on such a space. Using the covariant coordinate technique, we build a gauge invariant action in which, according to the Seiberg-Witten map, the physical degrees of freedom are expressed in terms of their commutative counterparts up to the first order in noncommutative parameters.

More on the Nambu-Poisson M5-brane theory: scaling limit, background independence and an all order solution to the Seiberg-Witten map

We continue our investigation on the Nambu-Poisson description of M5-brane in a large constant C-field background (NP M5-brane theory) constructed in refs. [1, 2]. In this paper, the low energy limit where the NP M5-brane theory is applicable is clarified. The background independence of the NP M5-brane theory is made manifest using the variables in the BLG model of multiple M2-branes. An all order solution to the Seiberg-Witten map is also constructed.

ELECTROMAGNETIC EXCITATIONS OF An QUANTUM HALL DROPLETS

The classical description of An internal degrees of freedom is given by making use of the Fock–Bargmann analytical realization. The symplectic deformation of phase space, including the internal degrees of freedom, is discussed. We show that the Moser's lemma provides a mapping to eliminate the fluctuations of the symplectic structure, which become encoded in the Hamiltonian of the system. We discuss the relation between Moser and Seiberg–Witten maps. One physics application of this result is the electromagnetic excitation of a large collection of particles, obeying the generalized An statistics, living in the complex projective space CPk with U(1) background magnetic field. We explicitly calculate the bulk and edge actions. Some particular symplectic deformations are also considered.

Nonperturbative Effects on Seven-Brane Yukawa Couplings

We analyze nonperturbative corrections to the superpotential of seven-brane gauge theories on type IIB and F-theory warped Calabi-Yau compactifications. We show, in particular, that such corrections modify the holomorphic Yukawa couplings by an exponentially suppressed contribution, generically solving the Yukawa rank-one problem of certain F-theory local models. We provide explicit expressions for the nonperturbative correction to the seven-brane superpotential, and check that it is related to a noncommutative deformation to the tree-level superpotential via a Seiberg-Witten map.

UV/IR mixing via a Seiberg-Witten map for noncommutative QED

We consider quantum electrodynamics in noncommutative spacetime by deriving a $\theta$-exact Seiberg-Witten map with fermions in the fundamental representation of the gauge group as an expansion in the coupling constant. Accordingly, we demonstrate the persistence of UV/IR mixing in noncommutative QED with charged fermions via Seiberg-Witten map, extending the results of Schupp and You [1].

Emergent noncommutative gravity from a consistent deformation of gauge theory

Starting from a standard noncommutative gauge theory and using the Seiberg-Witten map we propose a new version of a noncommutative gravity. We use consistent deformation theory starting from a free gauge action and gauging a killing symmetry of the background metric to construct a deformation of the gauge theory that we can relate with gravity. The result of this consistent deformation of the gauge theory is nonpolynomial in A_\mu. From here we can construct a version of noncommutative gravity that is simpler than previous attempts. Our proposal is consistent and is not plagued with the problems of other approaches like twist symmetries or gauging other groups.

On the energy crisis in noncommutative [formula omitted] model

We study the CP ( 1 ) system in ( 2 + 1 ) -dimensional noncommutative space with and without Chern–Simons term. Using the Seiberg–Witten map we convert the noncommutative CP ( 1 ) system to an action written in terms of the commutative fields. We find that this system presents the same infinite size instanton solution as the commutative Chern–Simons- CP ( 1 ) model without a potential term. Based on this result we argue that the BPS equations are compatible with the full variational equations of motion, rejecting the hypothesis of an “energy crisis”. In addition we examine the noncommutative CP ( 1 ) system with a Chern–Simons interaction. In this case we find that when the theory is transformed by the Seiberg–Witten map it also presents the same instanton solution as the commutative Chern–Simons- CP ( 1 ) model.

Non-linearly extended self-dual relations from the Nambu-bracket description of M5-brane in a constant C-field background

The derivation of the self-dual relations for the two-form gauge field in the Nambu-bracket description of M5-brane in a constant C-field background initiated in arXiv:0907.4596 is completed by including contributions from all the fields in the M5-brane action. The result is used to examine Seiberg-Witten map of the BPS conditions for the string solitons, up to the first order in the expansion by the parameter $g$ which characterizes the strength of the interactions through the Nambu-bracket.

Coordinate Dependence of Chern-Simons Theoryon Noncommutative AdS3

We investigate the coordinate dependence of noncommutative theory by studying the solutions of noncommutative U(1, 1)× U(1, 1) Chern-Simons theory on AdS3 in polar and rectangular coordinates. We assume that only the space coordinates are noncommuting. When the two coordinate systems are equivalent only up to first order in the noncommutativity parameter θ, we investigate the effect of this non-exact equivalence between the two coordinate systems for two cases, a conical solution and a BTZ black hole solution in noncommutative AdS3, by using the Seiberg-Witten map. In each case, the noncommutative solutions in the two coordinate systems obtained from the same corresponding commutative solution turn out to be different even to the first order in θ.

Canonical approach to noncommutative gauge theory

It is known that gauge transformation of the Kalb–Ramond field Bμν with vector parameter Λμ is symmetry of the closed string world-sheet action. It fails at the end points of the open string and can be restored by introducing Maxwell field Aμ. We show that the same conclusion valid for space–time equations of motion, because they are conditions for conformal invariance of the world-sheet action. This is example how the symmetries of space–time theory can be investigated using properties of σ-model energy–momentum tensor. We also show that the reducible part of the closed string symmetry transformation, with Λμ=∂μλ, turns to irreducible part of the open string one. As well as Maxwell field Aμ, the parameter λ is nontrivial only on the string endpoints. We show that after quantization the symmetry transformations of the background fields Bμν and Aμ turn to the modified symmetries defined in terms of Moyal star product. The modified Λμ-transformation related different regularizations as well as Seiberg–Witten map.

Noncommutative 𝒩 = 1 super Yang-Mills, the Seiberg-Witten map and UV divergences

Classically, the dual under the Seiberg-Witten map of noncommutative U(N), {\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a \theta-deformed nonlinear realisation of the {\cal N}=1 supersymmetry algebra in four dimensions. For the latter theory we work out at one-loop and first order in the noncommutative parameter matrix \theta^{\mu\nu} the UV divergent part of its effective action in the background-field gauge, and, for N>=2, we show that for finite values of N the gauge sector fails to be renormalisable; however, in the large N limit the full theory is renormalisable, in keeping with the expectations raised by the quantum behaviour of the theory's noncommutative classical dual. We also obtain --for N>=3, the case with N=2 being trivial-- the UV divergent part of the effective action of the SU(N) noncommutative theory in the enveloping-algebra formalism that is obtained from the previous ordinary U(N) theory by removing the U(1) degrees of freedom. This noncommutative SU(N) theory is also renormalisable.

Can Seiberg–Witten map bypass noncommutative gauge theory no-go theorem?

There are strong restrictions on the possible representations and in general on the matter content of gauge theories formulated on noncommutative Moyal spaces, termed as noncommutative gauge theory no-go theorem. According to the no-go theorem (Chaichian, Prešnajder, Sheikh-Jabbari and Tureanu, 2002) [1], matter fields in the noncommutative U ( 1 ) gauge theory can only have ±1 or zero charges and for a generic noncommutative ∏ i = 1 n U ( N i ) gauge theory matter fields can be charged under at most two of the U ( N i ) gauge group factors. On the other hand, it has been argued in the literature that, since a noncommutative U ( N ) gauge theory can be mapped to an ordinary U ( N ) gauge theory via the Seiberg–Witten map, seemingly it can bypass the no-go theorem. In this note we show that the Seiberg–Witten map (Seiberg and Witten, 1999) [2] can only be consistently defined and used for the gauge theories which respect the no-go theorem. We discuss the implications of these arguments for the particle physics model building on noncommutative space.

EMERGENT GRAVITY FROM NONCOMMUTATIVE SPACE–TIME

We showed before that self-dual electromagnetism in noncommutative (NC) space–time is equivalent to self-dual Einstein gravity. This result implies a striking picture about gravity: gravity can emerge from electromagnetism in NC space–time. Gravity is then a collective phenomenon emerging from gauge fields living in fuzzy space–time. We elucidate in some detail why electromagnetism in NC space–time should be a theory of gravity. In particular, we show that NC electromagnetism is realized through the Darboux theorem as a diffeomorphism symmetry G which is spontaneously broken to symplectomorphism H due to a background symplectic two-form Bμν = (1/θ)μν, giving rise to NC space–time. This leads to a natural speculation that the emergent gravity from NC electromagnetism corresponds to a nonlinear realization G/H of the diffeomorphism group, more generally its NC deformation. We also find some evidences that the emergent gravity contains the structures of generalized complex geometry and NC gravity. To illuminate the emergent gravity, we illustrate how self-dual NC electromagnetism nicely fits with the twistor space describing curved self-dual space–time. We also discuss derivative corrections of Seiberg–Witten map which give rise to higher-order gravity.

Remarks on an exact Seiberg-Witten map

We obtain the leading derivative corrections to an expression for the Seiberg-Witten map given by Banerjee and Yang and show how they affect the noncommutative deformation of the Maxwell action, as well as the matter coupling in noncommutative emergent gravity.