Piljin Yi

Monopoles and instantons on partially compactified D -branes

Motivated by the recent D-brane constructions of world-volume monopoles and instantons, we study the supersymmetric SU(N) Yang-Mills theory on S{sup 1}{times}R{sup 3+1}, spontaneously broken by a Wilson loop. In addition to the usual N{minus}1 fundamental monopoles, the Nth Bogomol{close_quote}nyi-Prasad-Sommerfield monopole appears from the Kaluza-Klein sector. When all N monopoles are present, net magnetic charge vanishes and the solution can be reinterpreted as a Wilson-loop instanton of unit Pontryagin number. The instanton-multimonopole moduli space is explicitly constructed, and seen to be identical to a Coulomb phase moduli space of a U(1){sup N} gauge theory in 2+1 dimensions related to Kronheimer{close_quote}s gauge theory of SU(N)-type. This extends the results by Intriligator and Seiberg to the finite couplings that, in the infrared limit of Kronheimer{close_quote}s theory, the Coulomb phase parametrizes a centered SU(N) instanton. We also elaborate on the case of restored SU(N) symmetry. {copyright} {ital 1997} {ital The American Physical Society}

Witten index and threshold bound states of D-branes

We consider the Witten index I = Tr(−1)F of SU(2) super Yang-Mills quantum mechanics (SYMQ) with N = 16, 8, 4 supersymmetries. The theory governs the interactions between a pair of D-branes under various circumstances, and our goal is to count the number of the threshold bound states directly from the low-energy effective theory. String theory and M-theory have predicted that I = 1 for N = 16, which in fact forms an underlying hypothesis of the M(atrix)-theory formulation. Also the consistency of conifold transitions in type II theories is known to require I = 0 for N = 8 and 4. Here, the bulk contribution to I is computed explicitly, and for N = 16, 8, 4, found to be 54, 14, 14 respectively, suggesting a common defect contribution of −14. We illustrate how the defect term of −14 may arise in the SU(2) SYMQ by considering the effective dynamics along the asymptotic region.

Moduli space of many BPS monopoles for arbitrary gauge groups

We study the moduli space for an arbitrary number of BPS monopoles in a gauge theory with an arbitrary gauge group that is maximally broken to U(1){sup {ital k}}. From the low energy dynamics of well-separated dyons we infer the asymptotic form of the metric for the moduli space. For a pair of distinct fundamental monopoles, the space thus obtained is {ital R}{sup 3}{times}({ital R}{sup 1}{times}{ital M}{sub 0})/{ital Z}, where {ital M}{sub 0} is the Euclidean Taub-NUT manifold. Following the methods of Atiyah and Hitchin, we demonstrate that this is actually the exact moduli space for this case. For any number of such objects, we show that the asymptotic form remains nonsingular for all values of the intermonopole distances and that it has the symmetries and other characteristics required of the exact metric. We, therefore, conjecture that the asymptotic form is exact for these cases also. {copyright} {ital 1996 The American Physical Society.}

Electromagnetic duality and SU(3) monopoles

Abstract We consider the low-energy dynamics of a pair of distinct fundamental monopoles that arise in the N = 4 supersymmetric SU (93) Yang-Mills theory broken to U (1) × U (1). Both the long distance interactions and the short distance behavior indicate that the moduli space is R 3 × (R 1 × M 0 ) Z where M 0 is the smooth Taub-NUT manifold, and we confirm this rigorously. By examining harmonic forms on the moduli space, we find a threshold bound state of two monopoles with a tower of BPS dyonic states built on it, as required by Montonen-Olive duality. We also present a conjecture for the metric of the moduli space for any number of distinct fundamental monopoles for an arbitrary gauge group.

Four-dimensional BPS spectra via M theory

We consider the realization of four-dimensional theories with N=2 supersymmetry as M-theory configurations including a five-brane. Our emphasis is on the spectrum of massive states that are realized as two-branes ending on the five-brane. We start with a determination of the supersymmetries that are left unbroken by the background metric and five-brane. We then show how the central charge of the N=2 algebra arises from the central charge associated with the M-theory two-brane. This determines the condition for a two-brane configuration to be BPS saturated in the four-dimensional sense. By imposing certain conditions on the moduli, we can give concrete examples of such two-branes. This leads us to conjecture that vector multiplet and hypermultiplet BPS-saturated states correspond to two-branes with the topology of a cylinder and a disk, respectively. {copyright} {ital 1997} {ital The American Physical Society}

Massive and massless monopoles with non-Abelian magnetic charges

We use the multimonopole moduli space as a tool for studying the properties of BPS monopoles carrying non-Abelian magnetic charges. For configurations whose total magnetic charge is purely Abelian, the moduli space for non-Abelian breaking can be obtained as a smooth limit of that for a purely Abelian breaking. As the asymptotic Higgs field is varied toward one of the special values for which the unbroken symmetry is enlarged to a non-Abelian group, some of the fundamental monopoles of unit topological charge remain massive but acquire non-Abelian magnetic charges. The BPS mass formula indicates that others should become massless in this limit. We find that these do not correspond to distinct solitons but instead manifest themselves as {open_quote}{open_quote}non-Abelian clouds{close_quote}{close_quote} surrounding the massive monopoles. The moduli space coordinates describing the position and U(1) phase of these massless monopoles are transformed into an equal number of non-Abelian global gauge orientation and gauge-invariant structure parameters characterizing the non-Abelian cloud. We illustrate this explicitly in a class of Sp(2{ital N}) examples for which the full family of monopole solutions is known. We show in detail how the unbroken symmetries of the theory are manifested as isometries of the moduli space metric. We discuss themorexa0» connection of these results to the Montonen-Olive duality conjecture, arguing in particular that the massless monopoles should be understood as the duals to the massless gauge bosons that appear as the mediators of the non-Abelian forces in the perturbative sector. {copyright} {ital 1996 The American Physical Society.}«xa0less

A Family of N=2 gauge theories with exact S duality

We study an infinite family of N = 2 Sp(2n) gauge theories that naturally arise from the D3-brane probe dynamics in F-theory. The matter sector consists of four fundamental and one antisymmetric tensor hypermultiplets. We propose that, in the limit of vanishing bare masses, the theory has exact SO(8) ⋉ SL(2, Z) duality. We examine the semiclassical BPS spectrum in the Coulomb phase by quantizing various monopole moduli space dynamics, and show that it is indeed consistent with the exact S-duality.

Quantum stability of accelerated black holes.

We study quantum aspects of the accelerated black holes in some detail. Explicitly shown is the fact that a uniform acceleration stabilizes certain charged black holes against the well-known thermal evaporation. Furthermore, a close inspection of the geometry reveals that this is possible only for near-extremal black holes and that most nonextremal varieties continue to evaporate with a modified spectrum under the acceleration. We also introduce a two-dimensional toy model where the energy-momentum flow is easily obtained for general accelerations, and find the behavior to be in accordance with the four-dimensional results. After a brief comparison to the classical system of a uniformly accelerated charge, we close by pointing out the importance of this result in the WKB expansion of the black hole pair-creation rate.

Self-dual anyons in uniform background fields

We study relativistic self-dual Chern-Simons-Higgs systems in the presence of uniform background fields that explicitly break {ital CTP}. A rich, but discrete vacuum structure is found when the gauge symmetry is spontaneously broken, while the symmetric phase can have an infinite vacuum degeneracy at the tree level. The latter is due to the proliferation of neutral solitonic states that cost zero energy. Various novel self-dual solitons, such as these, are found in both the symmetric and the asymmetric phases. Also by considering a similar system on a two-sphere and the subsequent large sphere limit we isolate sensible and finite expressions for the conserved angular and linear momenta, which satisfy anomalous commutation relations. We conclude with a few remarks on unresolved issues.

Vanishing Hawking radiation from a uniformly accelerated black hole.

We consider quantum fields around uniformly accelerated black holes. At a particular value of the acceleration, the Bogolubov transformation which would be responsible for the late-time Hawking radiation, is found to be trivial. When this happens, Hawkings thermal radiation, Doppler-shifted or not, is absent to the asymptotic inertial observers despite the nonzero Hawking temperature, while the co-moving observers find the black hole radiance exactly balanced by the acceleration heat bath. After a brief comparison to the classical system of a uniformly accelerated charge, we close with two important comments. (Phys. Rev. Lett. 75 (1995) 382)