Results 1  10
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30
Monopoles and four manifolds
 Math.Res. Lett
, 1994
"... Recent developments in the understanding of N = 2 supersymmetric YangMills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining fourmanifold invariants by counting SU(2) instantons, one can define equivalent fourmanifold invariants by ..."
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Recent developments in the understanding of N = 2 supersymmetric YangMills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining fourmanifold invariants by counting SU(2) instantons, one can define equivalent fourmanifold invariants by counting solutions of a nonlinear equation with an abelian gauge group. This is a “dual ” equation in which the gauge group is the dual of the maximal torus of SU(2). The new viewpoint suggests many new results about the Donaldson invariants. November
Marginal and relevant deformations of N=4 field theories and noncommutative moduli spaces of vacua”, JHEP 0005
, 2000
"... Abstract: We study marginal and relevant supersymmetric deformations of the N = 4 superYangMills theory in four dimensions. Our primary innovation is the interpretation of the moduli spaces of vacua of these theories as noncommutative spaces. The construction of these spaces relies on the represe ..."
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Cited by 24 (3 self)
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Abstract: We study marginal and relevant supersymmetric deformations of the N = 4 superYangMills theory in four dimensions. Our primary innovation is the interpretation of the moduli spaces of vacua of these theories as noncommutative spaces. The construction of these spaces relies on the representation theory of the related quantum algebras, which are obtained from Fterm constraints. These field theories are dual to superstring theories propagating on deformations of the AdS5×S 5 geometry. We study Dbranes propagating in these vacua and introduce the appropriate notion of algebraic geometry for noncommutative spaces. The resulting moduli spaces of Dbranes have several novel features. In particular, they may be interpreted as symmetric products of noncommutative spaces. We show how mirror symmetry between these deformed geometries and orbifold theories follows from Tduality. Many features of the dual closed string theory may be identified within the noncommutative algebra. In particular, we make progress towards understanding the Ktheory necessary for backgrounds where the NeveuSchwarz antisymmetric tensor of the string is turned on, and we shed light on some aspects of discrete
NonSupersymmetric SO(3)Invariant Deformations of N = 1∗ Vacua and their Dual String Theory Description,” JHEP 0012 (2000) 021, hepth/0007082
 Itoh, “Dielectricbranes in Nonsupersymmetric SO(3)invariant Perturbation of Threedimensional N=8 YangMills Theory,” Phys. Rev. D64 (2001) 086006, hepth/0105044. 32
"... We study the SO(3)invariant relevant deformations of N = 4 SU(N) gauge theory using the methods of Polchinski and Strassler. We present the region of parameter space where the nonsupersymmetric vacuum is still described by stable “dielectric ” five branes within the supergravity approximation ..."
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We study the SO(3)invariant relevant deformations of N = 4 SU(N) gauge theory using the methods of Polchinski and Strassler. We present the region of parameter space where the nonsupersymmetric vacuum is still described by stable “dielectric ” five branes within the supergravity approximation
G2CalogeroMoser Lax operators from reduction
, 2005
"... We construct a Lax operator for the G2CalogeroMoser model by means of a double reduction procedure. In the first reduction step we reduce the A6model to a B3model with the help of an embedding of the B3root system into the A6root system together with the specification of certain coupling con ..."
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Cited by 4 (3 self)
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We construct a Lax operator for the G2CalogeroMoser model by means of a double reduction procedure. In the first reduction step we reduce the A6model to a B3model with the help of an embedding of the B3root system into the A6root system together with the specification of certain coupling constants. The G2Lax operator is obtained thereafter by means of an additional reduction by exploiting the embedding of the G2system into the B3system. The degree of algebraically independent and nonvanishing charges is found to be equal to the degrees of the corresponding Lie algebra.
On phases of gauge theories and the role of nonBPS solitons in field theory,” arXiv:hepth/9808073
"... As shown in hepth/9709081, 1 nonBPS saturated solitons play an important role in the duality transformations ofN = 1 supersymmetric gauge theories. In particular, a massive spinor in an SO(N) gauge theory with massless matter in the vector representation appears in the dual description as a magnet ..."
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Cited by 4 (0 self)
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As shown in hepth/9709081, 1 nonBPS saturated solitons play an important role in the duality transformations ofN = 1 supersymmetric gauge theories. In particular, a massive spinor in an SO(N) gauge theory with massless matter in the vector representation appears in the dual description as a magnetic monopole with a Z2 charge. This claim is supported by numerous tests, including detailed matching of flavor quantum numbers. This fact makes it possible to test the phase of an SO(N) gauge theory using massive spinors as a probe. It is thereby shown explicitly that the free magnetic phase which appears in supersymmetric theories is a nonconfining phase. A fully nonabelian version of the Dual Meissner effect is also exhibited, in which the monopoles are confined by nonBPS string solitons with Z2 charges. a a Talk given at the third workshop on ”Continuous Advances in QCD”, University
On emergence in gauge theories at the ’t Hooft limit
, 2012
"... Quantum field theories are notoriously difficult to understand, physically as well as philosophically. The aim of this paper is to contribute to a better conceptual understanding of gauge quantum field theories, such as quantum chromodynamics, by discussing a famous physical limit, the ’t Hooft limi ..."
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Quantum field theories are notoriously difficult to understand, physically as well as philosophically. The aim of this paper is to contribute to a better conceptual understanding of gauge quantum field theories, such as quantum chromodynamics, by discussing a famous physical limit, the ’t Hooft limit, in which the theory concerned often simplifies. The idea of the limit is that the number N of colours (or charges) goes to infinity. The simplifications that can happen in this limit, and that we will consider, are: (i) the theory’s Feynman diagrams can be drawn on a plane without lines intersecting (called ‘planarity’); and (ii) the theory, or a sector of it, becomes integrable, and indeed corresponds to a wellstudied system, viz. a spin chain. Planarity is important because it shows how a quantum field theory can exhibit extended, in particular stringlike, structures; in some cases, this gives a connection with string theory, and thus with gravity. Previous philosophical literature about how one theory (or a sector, or regime, of a theory) might be emergent from, andor reduced to, another one has tended to emphasize cases, such as occur in statistical mechanics, where the system before the limit has finitely many degrees of freedom. But here, our quantum field theories, including those on the way to the ’t Hooft limit, will have infinitely many degrees of freedom. Nevertheless, we will show how a recent schema by Butterfield and taxonomy by Norton apply to the quantum field theories we consider; and we will classify three physical properties of our theories in these terms. These properties are planarity and integrability, as in (i) and (ii) above; and the behaviour of the betafunction reflecting, for example, asymptotic freedom. Our discussion of these properties, especially the betafunction, will also relate to recent philosophical debate about the propriety of assessing quantum field theories, whose rigorous existence is not yet proven.
SU(5)invariant decomposition of tendimensional YangMills supersymmetry,” Phys
 Lett. B 698
, 2011
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On the relationship between the RozanskyWitten and the threedimensional SeibergWitten invariants
 Adv. Theor. Math. Phys
"... The SeibergWitten analysis of the lowenergy effective action of d = 4 N = 2 SYM theories reveals the relation between the Donaldson and SeibergWitten (SW) monopole invariants. Here we apply analogous reasoning to d = 3 N = 4 theories and propose a general relationship between RozanskyWitten (RW) ..."
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The SeibergWitten analysis of the lowenergy effective action of d = 4 N = 2 SYM theories reveals the relation between the Donaldson and SeibergWitten (SW) monopole invariants. Here we apply analogous reasoning to d = 3 N = 4 theories and propose a general relationship between RozanskyWitten (RW) and 3dimensional Abelian monopole invariants. In particular, we deduce the equality of the SU(2) Casson invariant and the 3dimensional SW invariant (this includes a special case of the MengTaubes theorem relating the SW invariant to Milnor torsion). Since there are only a finite number of basic RW invariants of a given degree, many different topological field theories can be used to represent essentially the same topological invariant. This leads us to advocate using higher rank Abelian gauge theories to shed light on the higher (nonAbelian) RW invariants and we write down candidate higher rank SW equations. 1
unknown title
, 2005
"... EPJ manuscript No. (will be inserted by the editor) High pT leading hadron suppression in nuclear collisions at sNN ≈ 20 – 200 GeV: data versus parton energy loss models ..."
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EPJ manuscript No. (will be inserted by the editor) High pT leading hadron suppression in nuclear collisions at sNN ≈ 20 – 200 GeV: data versus parton energy loss models