Seiberg-Witten Research Articles

Duality between Seiberg-Witten theory and black hole superradiance

The newly established Seiberg-Witten (SW)/Quasinormal Modes (QNM) correspondence offers an efficient analytical approach to calculate the QNM frequencies, which was only available numerically before. This is based on the fact that both sides are characterized by Heun-type equations. We find that a similar duality exists between Seiberg-Witten theory and black hole superradiance, since the latter can also be linked to confluent Heun equation after proper transformation. Then a dictionary is constructed, with the superradiance frequencies written in terms of gauge parameters. Further by instanton counting, and taking care of the boundary conditions through connection formula, the relating frequencies are obtained analytically, which show consistency with known numerical results.

Schwarzschild black hole surrounded by a cavity and phase transition in the non-commutative gauge theory of gravity

In this work, we investigate the phase transition of the Schwarzschild black hole (SBH) inside an isothermal spherical cavity in the context of the non-commutative (NC) gauge theory of gravity, by using the Seiberg–Witten (SW) map and the star product. Firstly, we compute the NC correction to the Hawking temperature and derive the logarithmic correction to the entropy, then we derive the local temperature and local energy of NC SBH in isothermal cavity. Our results show that the non-commutativity removes the commutative divergence behavior of temperature, and prevents the SBH from the complete evaporation, which leads to a remnant black hole, and this geometry has predicted a minimal length in the order of Planck scale Θ∼lplanck. Therefore, the thermodynamic stability and phase transition is studied by analyzing the behavior of the local heat capacity and the Helmholtz free energy in the NC spacetime, where the results show that, the NC SBH has a two second-order phase transition and one first-order phase transition, with two Hawking–Page phase transition in the NC gauge theory.

Quantum tunneling from Schwarzschild black hole in non-commutative gauge theory of gravity

In this letter, we present the first study of Hawking radiation as a tunneling process within the framework of non-commutative (NC) gauge theory of gravity. First, we reconstruct the non-commutative Schwarzschild black hole (NC SBH) within the gauge theory of gravity, employing the Seiberg-Witten (SW) map and the star product. Then, we compute the emission spectrum of outgoing massless particles using the quantum tunneling mechanism. In the first scenario, we calculate the tunneling rate of massless particles crossing the event horizon of the NC SBH with lower frequencies. Our results reveal pure thermal radiation. Notably, we find that the Hawking temperature remains consistent in both the classical thermodynamics and the quantum tunneling approach, suggesting equivalence between these two approaches in NC spacetime. However, in the case of massless particle emission with higher frequencies, we account for energy conservation resulting in the tunneling rate to deviate from pure thermal radiation. This tunneling rate remains consistent with an underlying unitary quantum theory. We establish a relationship between this deviation and the change in the black hole entropy, revealing a logarithmic correction to the entropy within this geometry. Furthermore, we demonstrate that non-commutativity enhances the correlations between two successively emitted particles. Additionally, we determine the NC density number of particle emission and conclude by discussing the implications of our findings.

Charge instability of JMaRT geometries

We perform a detailed study of linear perturbations of the JMaRT family of non-BPS smooth horizonless solutions of type IIB supergravity beyond the near-decoupling limit. In addition to the unstable quasi normal modes (QNMs) responsible for the ergo-region instability, already studied in the literature, we find a new class of ‘charged’ unstable modes with positive imaginary part, that can be interpreted in terms of the emission of charged (scalar) quanta with non zero KK momentum. We use both matched asymptotic expansions and numerical integration methods. Moreover, we exploit the recently discovered correspondence between JMaRT perturbation theory, governed by a Reduced Confluent Heun Equation, and the quantum Seiberg-Witten (SW) curve of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SYM theory with gauge group SU(2) and Nf = (0, 2) flavours.

More on Seiberg-Witten theory and Monstrous moonshine: A new simple method of calculating the prepotential

We continue the study of a relationship between the instanton expansion of the Seiberg-Witten (SW) prepotential of D=4, N=2SU(2) SUSY gauge theory and the Monstrous moonshine. As was done in [10], we expand the inverse of the modular j-function in u−1 around u=∞, where u is the familiar u parameter for the respective SW curves, and compute the complex gauge coupling τ as a function of the scalar vev a by using the Fourier expansion of j(τ) and the relation between u and a obtained by the Picard-Fuchs equation. In this way, the instanton expansion of the prepotential is related to the dimensions of representations of the Monster group. We show that, for the cases of Nf=2 and 3, q again has an expansion whose coefficients are all integer-coefficient polynomials of the moonshine coefficients if the expansion variables are appropriately chosen. This hints some unknown relation between the Liouville CFT and the vertex operator algebra CFT with different central charges. We also demonstrate that this new method of calculating the SW prepotential developed here is useful by performing some explicit computations.

Klein-Gordon Theory in Noncommutative Phase Space

We extend the three-dimensional noncommutative relations of the position and momentum operators to those in the four dimension. Using the Seiberg-Witten (SW) map, we give the Heisenberg representation of these noncommutative algebras and endow the noncommutative parameters associated with the Planck constant, Planck length and cosmological constant. As an analog with the electromagnetic gauge potential, the noncommutative effect can be interpreted as an effective gauge field, which depends on the Plank constant and cosmological constant. Based on these noncommutative relations, we give the Klein-Gordon (KG) equation and its corresponding current continuity equation in the noncommutative phase space including the canonical and Hamiltonian forms and their novel properties beyond the conventional KG equation. We analyze the symmetries of the KG equations and some observables such as velocity and force of free particles in the noncommutative phase space. We give the perturbation solution of the KG equation.

Seiberg–Witten theory and monstrous moonshine

Abstract We study the relation between the instanton expansion of the Seiberg–Witten (SW) prepotential for D = 4, ${\cal N}=2$SU(2) SUSY gauge theory for Nf = 0 and 1 and the monstrous moonshine. By utilizing a newly developed simple method to obtain the SW prepotential, it is shown that the coefficients of the expansion of q = e2πiτ in terms of $A^2=\frac{\Lambda ^2}{16 a^2}$ (Nf = 0) or $\frac{\Lambda ^2}{32a^2}$ (Nf = 1) are all integer-coefficient polynomials of the moonshine coefficients of the modular j-function. A relationship between the Alday–Gaiotto–Tachikawa (AGT) c = 25 Liouville conformal field theory (CFT) and the c = 24 vertex operator algebra CFT of the moonshine module is also suggested.

Seiberg-Witten maps and scattering amplitudes of noncommutative QED

The connection between tree-level scattering amplitudes and the Seiberg-Witten (SW) map in the Moyal deformed U(1) noncommutative quantum electrodynamics (NCQED) is studied. We show that in the minimal U(1) NCQED based on a reversible Seiberg-Witten (SW) map, SW map induced interactions cancel each other in all tree-level scattering amplitudes and leave them identical to the Moyal NCQED without SW map. On the other hand, the two-by-two Compton and light-by-light scattering amplitudes deviate from minimal model when irreversible SW map is used. Therefore the reversibility of SW map and equivalence between NCQED before and after SW map manifest as an identity between the tree-level scattering amplitudes.

The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories

The simplest non-trivial 5d superconformal field theories (SCFT) are the famous rank-one theories with E_nEn flavour symmetry. We study their UU-plane, which is the one-dimensional Coulomb branch of the theory on \mathbb{R}^4 \times S^1ℝ4×S1. The total space of the Seiberg-Witten (SW) geometry – the E_nEn SW curve fibered over the UU-plane – is described as a rational elliptic surface with a singular fiber of type I_{9-n}I9−n at infinity. A classification of all possible Coulomb branch configurations, for the E_nEn theories and their 4d descendants, is given by Persson’s classification of rational elliptic surfaces. We show that the global form of the flavour symmetry group is encoded in the Mordell-Weil group of the SW elliptic fibration. We study in detail many special points in parameters space, such as points where the flavour symmetry enhances, and/or where Argyres-Douglas and Minahan-Nemeschansky theories appear. In a number of important instances, including in the massless limit, the UU-plane is a modular curve, and we use modularity to investigate aspects of the low-energy physics, such as the spectrum of light particles at strong coupling and the associated BPS quivers. We also study the gravitational couplings on the UU-plane, matching the infrared expectation for the couplings A(U)A(U) and B(U)B(U) to the UV computation using the Nekrasov partition function.

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.

Machine-learning dessins d’enfants: explorations via modular and Seiberg–Witten curves

We apply machine-learning to the study of dessins d’enfants. Specifically, we investigate a class of dessins which reside at the intersection of the investigations of modular subgroups, Seiberg–Witten (SW) curves and extremal elliptic K3 surfaces. A deep feed-forward neural network with simple structure and standard activation functions without prior knowledge of the underlying mathematics is established and imposed onto the classification of extension degree over the rationals, known to be a difficult problem. The classifications reached 0.92 accuracy with 0.03 standard error relatively quickly. The SW curves for those with rational coefficients are also tabulated.

Integrability and cycles of deformed [formula omitted] gauge theory

To analyse pure N=2SU(2) gauge theory in the Nekrasov-Shatashvili (NS) limit (or deformed Seiberg-Witten (SW)), we use the Ordinary Differential Equation/Integrable Model (ODE/IM) correspondence, and in particular its (broken) discrete symmetry in its extended version with two singular irregular points. Actually, this symmetry appears to be ‘manifestation’ of the spontaneously broken Z2 R-symmetry of the original gauge problem and the two deformed SW one-cycle periods are simply connected to the Baxter's T and Q functions, respectively, of the Liouville conformal field theory at the self-dual point. The liaison is realised via a second order differential operator which is essentially the ‘quantum’ version of the square of the SW differential. Moreover, the constraints imposed by the broken Z2 R-symmetry acting on the moduli space (Bilal-Ferrari equations) seem to have their quantum counterpart in the TQ and the T periodicity relations, and integrability yields also a useful Thermodynamic Bethe Ansatz (TBA) for the periods (Y(θ,±u) or their square roots, Q(θ,±u)). A latere, two efficient asymptotic expansion techniques are presented. Clearly, the whole construction is extendable to gauge theories with matter and/or higher rank groups.

Quantum Seiberg-Witten curve and universality in Argyres-Douglas theories

We study the quantum Seiberg-Witten (SW) curves for (A1,G)-type Argyres-Douglas (AD) theory by taking the scaling limit of the quantum SW curve of N=2 gauge theory with gauge group G. For G=Ar, the quantum SW curve of the AD theory is consistent with the scaling limit of the curve of the gauge theory. For G=Dr, we need the quantum correction to the SW curve of the AD theory, which depends on the quantization condition of the original SW curve. We also study the universality of the quantum SW curves for (A1,A3) and (A1,D4)-type AD theories.

SO(2,3)★ Noncommutative Gravity: Coupling with Matter Fields

In this paper, noncommutative gravity is treated as a gauge theory of the noncommutative $$SO{{(2,3)}_{ \star }}$$ group, while the noncommutativity is canonical. The Seiberg–Witten (SW) map is used to express noncommutative fields in terms of the corresponding commutative fields. In addition to pure gravity, we consider couplings to matter fields, in particular, to the Dirac and $$U(1)$$ gauge field. The analysis can be extended to non Abelian gauge fields and scalar fields.

Noncommutative SO(2,3)⋆ gravity: Noncommutativity as a source of curvature and torsion

Noncommutative (NC) gravity is constructed on the canonical noncommutative (Moyal-Weyl) space-time as a noncommutative $SO(2,3)_\star$ gauge theory. The NC gravity action consists of three different terms: the first term is of Mac-Dowell Mansouri type, while the other two are generalizations of the Einstein-Hilbert action and the cosmological constant term. The expanded NC gravity action is then calculated using the Seiberg-Witten (SW) map and the expansion is done up second order in the deformation parameter. We analyze in details the low energy sector of the full model. We calculate the equations of motion, discuss their general properties and present one solution: the NC correction to Minkowski space-time. Using this solution, we explain breaking of the diffeomorphism symmetry as a consequence of working in a particular coordinate system given by the Fermi normal coordinates.

Mathcal{N} = 2 S-duality revisited

Using the chiral algebra bootstrap, we revisit the simplest Argyres-Douglas (AD) generalization of Argyres-Seiberg S-duality. We argue that the exotic AD superconformal field theory (SCFT), {mathcal{T}}_{3,frac{3}{2}} , emerging in this duality splits into a free piece and an interacting piece, {mathcal{T}}_X , even though this factorization seems invisible in the Seiberg-Witten (SW) curve derived from the corresponding M5-brane construction. Without a Lagrangian, an associated topological field theory, a BPS spectrum, or even an SW curve, we nonetheless obtain exact information about {mathcal{T}}_X by bootstrapping its chiral algebra, {}_{mathcal{X}}left({mathcal{T}}_Xright) , and finding the corresponding vacuum character in terms of Affine Kac-Moody characters. By a standard 4D/2D correspondence, this result gives us the Schur index for {mathcal{T}}_X and, by studying this quantity in the limit of small S1, we make contact with a proposed S1 reduction. Along the way, we discuss various properties of {mathcal{T}}_X : as an mathcal{N} = 1 theory, it has flavor symmetry SU(3) × SU(2) × U(1), the central charge of {}_{mathcal{X}}left({mathcal{T}}_Xright) matches the central charge of the bc ghosts in bosonic string theory, and its global SU(2) symmetry has a Witten anomaly. This anomaly does not prevent us from building conformal manifolds out of arbitrary numbers of {mathcal{T}}_X theories (giving us a surprisingly close AD relative of Gaiotto’s TN theories), but it does lead to some open questions in the context of the chiral algebra/4D mathcal{N} =2SCFT correspondence.

Generalized Seiberg-Witten Equations on a Riemann Surface

In this paper we consider twice-dimensionally reduced, generalized Seiberg-Witten (S-W) equations, defined on a compact Riemann surface. A novel feature of the reduction technique is that the resulting equations produce an extra “Higgs field”. Under suitable regularity assumptions, we show that the moduli space of gauge-equivalent classes of solutions to the reduced equations, is a smooth Kahler manifold and construct a pre-quantum line bundle over the moduli space of solutions.

Pauli equation on noncommutative plane and the Seiberg–Witten map

We study the Pauli equation in noncommutative (NC) two-dimensional plane which exhibits the supersymmetry (SUSY) algebra when the gyro-magnetic ratio is 2. The significance of the Seiberg–Witten (SW) map in this context is discussed and its effect in the problem is incorporated to all orders in [Formula: see text]. We map the NC problem to an equivalent commutative problem by using a set of generalized Bopp-shift transformations containing a scaling parameter. The energy spectrum of the NC Pauli Hamiltonian is obtained and found to be [Formula: see text] corrected which is valid to all orders in [Formula: see text].

Super Yang-Mills and θ-exact Seiberg-Witten map: absence of quadratic noncommutative IR divergences

We compute the one-loop 1PI contributions to all the propagators of the noncommutative (NC) $$ \mathcal{N}=1,2,4 $$ super Yang-Mills (SYM) U(1) theories defined by the means of the θ-exact Seiberg-Witten (SW) map in the Wess-Zumino gauge. Then we extract the UV divergent contributions and the noncommutative IR divergences. We show that all the quadratic noncommutative IR divergences add up to zero in each propagator.

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.