Exact Seiberg-Witten Research Articles

Seiberg-Witten map invariant scatterings

We investigate Scattering amplitudes of the reversible $\theta$-exact Seiberg-Witten (SW) map based noncommutative (NC) quantum electrodynamics, and show explicitly the SW map invariance for all tree-level NCQED $2\to2$ proceses, including M\"oller, Bhabha, Compton, pair annihilation, pair production and light-by-light $(\gamma\gamma\to\gamma\gamma)$ scatterings. We apply our NCQED results to the $\gamma\gamma\to\gamma\gamma$ and $\gamma\gamma\to\ell^+\ell^-$ exclusive processes, convoluted to the ultraperipheral lead $^{208}$Pb ion-ion collisions, recently measured by the ATLAS collaboration at LHC. We demonstrate that $\gamma\gamma\to\gamma\gamma$ is the more appropriate channel to probe NC scale $\Lambda_{\rm NC}$ while both are less efficient than some other probes.

Equivalence of quantum field theories related by theθ-exact Seiberg-Witten map

The equivalence of the noncommutative U(N) quantum field theories related by the theta-exact Seiberg-Witten maps is in this letter proven to all orders in the perturbation theory with respect to the coupling constant. We show that this duality holds for Super Yang-Mills theories with N=0,1,2,4 supersymmetry. A direct check of this equivalence relation is performed by computing the one-loop quantum corrections to the quadratic part of the effective action in the noncommutative U(1) gauge theory with N=0,1,2,4 supersymmetry.

Photon self-interaction on deformed spacetime

A novel nonlocal four-photon interaction on the deformed spacetime is derived and studied in the three selected models (I, II, III). The first two models (I, II) are obtained via two distinct second-order $\theta$-exact Seiberg-Witten maps of the noncommutative U(1) gauge field strength on Moyal space. The third one (III), inspired by the manifestly gauge invariant structures emerging in the first two, due to the model generality has been constructed with a different set of freedom parameters. The physical relevancy of all models is analyzed by evaluating the four-photon-tadpole diagram, which, when combined with the bubble graph, enables us to fully consider all contributions to the one-loop photon polarization tensor. For an arbitrary noncommutative matrix theta^\mu\nu, the full quadratic IR divergence cancellation in the one-loop photon two-point function is obtained with particular combinations of Seiberg-Witten map/gauge-symmetry freedom parameters in models I and II. Finally, our model III enables complete elimination of all pathological terms in the photon polarization tensor at one-loop order if a special value for the theta matrix is chosen.

θ-exact Seiberg-Witten maps at ordere3

We study two distinct $\ensuremath{\theta}$-exact Seiberg-Witten (SW) map expansions, (I) and (II), respectively, up to order ${e}^{3}$ for the gauge parameter, gauge field, and gauge field strengths of the noncommutative ${\mathrm{U}}_{\ensuremath{\star}}(1)$ gauge theory on the Moyal space. We derive explicitly the closed-form expression for the SW map ambiguity between the two and observe the emergence of several new totally commutative generalized star products. We also identify the additional gauge freedoms within each of the ${e}^{3}$-order field-strength expansions and define corresponding sets of deformation/ratio/weight parameters, $(\ensuremath{\kappa},{\ensuremath{\kappa}}_{i})$ and $(\ensuremath{\kappa},{\ensuremath{\kappa}}_{i}^{\ensuremath{'}})$, for these two SW maps, respectively.

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].

EXACT SEIBERG–WITTEN MAP AND INDUCED GRAVITY FROM NONCOMMUTATIVITY

We find a closed form for Seiberg–Witten (SW) map between ordinary and noncommutative (NC) Dirac–Born–Infeld actions. We show that NC Maxwell action after the exact SW map can be regarded as ordinary Maxwell action coupling to a metric deformed by gauge fields. We also show that reversed procedure by inverse SW map lead to a similar interpretation in terms of induced NC geometry. This implies that noncommutativity in field theory can be interpreted as field-dependent fluctuations of spacetime geometry, which genuinely realizes an interesting idea recently observed by Rivelles.

ALE spaces from noncommutative [formula omitted] instantons via exact Seiberg–Witten map

The exact Seiberg–Witten (SW) map of a noncommutative (NC) gauge theory gives the commutative equivalent as an ordinary gauge theory coupled to a field dependent effective metric. We study instanton solutions of this commutative equivalent whose self-duality equation turns out to be the exact SW map of NC instantons. We derive general differential equations governing U(1) instantons and we explicitly get an exact solution corresponding to the single NC instanton. Remarkably the effective metric induced by the single U(1) instanton is related to the Eguchi–Hanson metric—the simplest gravitational instanton. Surprisingly the instanton number is not quantized but depends on an integration constant. Our result confirms the expected non-perturbative breakdown of the SW map. However, the breakdown of the map arises in a consistent way: the instanton number plays the role of a parameter giving rise to a one-parameter family of Eguchi–Hanson metrics.

Exact Seiberg–Witten map, induced gravity and topological invariants in non-commutative field theories

We revisit the exact Seiberg–Witten (SW) map on Dirac–Born–Infeld actions, making a connection with the deformation quantization scheme. The picture on field dependent induced gravity from non-commutativity becomes more transparent in the context of deformation quantization. We also find an exact SW map for an adjoint scalar field, consistent with that deduced from RR couplings of unstable non-BPS D-branes. The dual description via the exact SW map can again be interpreted as the ordinary field theory coupling to gravity induced by gauge fields. Using the exact SW maps, we further discuss several aspects of topological invariants in non-commutative (NC) gauge theory. Especially, it is shown that the K-theory class on NC instantons is mapped to the usual second Chern class via exact SW map and it leads to an exact SW map between commutative and NC Chern–Simons terms.

Exact results in 5D from instantons and deconstruction

We consider non-perturbative effects in theories with extra dimensions and the deconstructed versions of these theories. We establish the rules for instanton calculations in 5D theories on the circle, and use them for an explicit one-instanton calculation in a supersymmetric gauge theory. The results are then compared to the known exact Seiberg-Witten type solution for this theory, confirming the validity both of the exact results and of the rules for instanton calculus for extra dimensions introduced here. Next we consider the non-perturbative results from the perspective of deconstructed extra dimensions. We show that the non-perturbative results of the deconstructed theory do indeed reproduce the known results for the continuum extra dimensional theory, thus providing the first non-perturbative evidence in favor of deconstruction. This way deconstruction also allows us to make exact predictions in higher dimensional theories which agree with earlier results, and helps to clarify the interpretation of 5D instantons.

CP, charge fractionalizations and low-energy effective actions in the SU(2) Seiberg-Witten theories with quarks

Several dynamical aspects of the SU(2) Seiberg-Witten models with Nf quark hypermultiplets are explored. We first clarify the meaning of the number of the singularities of the space of vacua. CP properties of the theories are then studied and periodicity of theories in θ with and without bare quark masses is obtained ((4- N f ) π and π respectively). CP noninvariance at a generic point of QMS manifests itself as the electric and quark-number charge fractionalizations for the dyons; we show that the exact Seiberg-Witten solution contains such effects correctly, in agreement with the semiclassical analysis recently made by F. Ferrari. Upon N = 1 perturbation the low-energy effective theories at the singularities display confinement, and in most cases chiral symmetry breaking as a consequence. In one of the vacua for N f = 3 confinement is not accompanied by chiral symmetry breaking: we interpret it as an example of oblique confinement of 't Hooft. We discuss further the consistency of the physical picture found here by studying the effects of soft supersymmetry breaking as well as the behavior of the theory in the N = 1 limit.

Solitons, Monopoles, and Duality: From Sine-Gordon to Seiberg-Witten

An elementary introduction into the Seiberg-Witten theory is given. Many efforts are made to get it as pedagogical as possible, within a reasonable size. The selection of the relevant material is heavily oriented towards graduate students. The basic ideas about solitons, monopoles, supersymmetry and duality are reviewed from first principles, and they are illustrated on the simplest examples. The exact Seiberg-Witten solution to the low-energy effective action of the four-dimensional N=2 supersymmetric pure Yang-Mills theory with the gauge group SU(2) is the main subject of the review. Other gauge groups are also considered. Some related issues (like adding matter, confinement, string dualities) are outlined.

Integrability and Seiberg-Witten exact solution

The exact Seiberg-Witten (SW) description of the light sector in the N = 2 SUSY 4 d Yang-Mills theory [N. Seiberg and E. Witten, Nucl. Phys. B 430 (1994) 485 (E); B 446 (1994) 19] is reformulated in terms of integrable systems and appears to be a Gurevich-Pitaevsky (GP) [A. Gurevich and L. Pitaevsky, JETP 65 (1973) 65; see also, S. Novikov, S. Manakov, L. Pitaevsky and V. Zakharov, Theory of solitons] solution to the elliptic Whitham equations. We consider this as an implication that the dynamical mechanism behind the SW solution is related to integrable systems on the moduli space of instantons. We emphasize the role of the Whitham theory as a possible substitute of the renormalization-group approach to the construction of low-energy effective actions.