Random Magnetic Fields, Supersymmetry, and Negative Dimensions

Parisi, Giorgio; Sourlas, Nicolas

doi:10.1103/physrevlett.43.744

Cited by 919 publications

(794 citation statements)

References 13 publications

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“…The proof of this statement is similar to that of Ref. [15]. The only difference of the case under study from the one considered in Ref.…”

Section: Dimensional Reduction In the Theory Which Confines Closed Stsupporting

confidence: 75%

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Confining membranes and dimensional reduction

Antonov¹

2001

J. High Energy Phys.

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The dual theory describing the 4D Coulomb gas of point-like magnetically charged objects, which confines closed electric strings, is considered. The respective generalization of the theory of confining strings to confining membranes is further constructed. The same is done for the analogous SU(3)-inspired model. We then consider a combined model which confines both electric charges and closed strings. Such a model is nothing, but the mixture of the above-mentioned Coulomb gas with the condensate of the dual Higgs field, described by the dual Abelian Higgs model. It is demonstrated that in a certain limit of this dual Abelian Higgs model, the system under study undergoes naively the dimensional reduction and becomes described by the (completely integrable) 2D sine-Gordon theory. In particular, owing to this fact, the phase transition in such a model must be of the Berezinskii-Kosterlitz-Thouless type, and the respective critical temperature is expressed in terms of the parameters of the dual Abelian Higgs model. However, it is finally discussed that the dimensional reduction is rigorously valid only in the strong coupling limit of the original 4D Coulomb gas. In such a limit, this reduction transforms the combined model to the 2D free bosonic theory. *

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“…The proof of this statement is similar to that of Ref. [15]. The only difference of the case under study from the one considered in Ref.…”

Section: Dimensional Reduction In the Theory Which Confines Closed Stsupporting

confidence: 75%

“…(15). Similarly to the SU(2)-inspired case, we obtain in the dilute gas approximation the nonlocal membrane action from the analogue of the full Wilson loop,…”

Section: Confining Membranesmentioning

confidence: 93%

Confining membranes and dimensional reduction

Antonov¹

2001

J. High Energy Phys.

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“…This is entirely analogous to what is done for spin glasses when one averages over background magnetic fields [22]. b) The solution A i (x) is a two-dimensional pure-gauge (in the sense that F ij = 0), but not also a four-dimensional pure-gauge, since the associated electric field…”

mentioning

confidence: 63%

The renormalization group equation for the color glass condensate

Iancu¹,

2001

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We present an explicit and simple form of the renormalization group equation which governs the quantum evolution of the effective theory for the Color Glass Condensate (CGC). This is a functional Fokker-Planck equation for the probability density of the color field which describes the CGC in the covariant gauge. It is equivalent to the Euclidean time evolution equation for a second quantized current-current Hamiltonian in two spatial dimensions. The quantum corrections are included in the leading log approximation, but the equation is fully non-linear with respect to the generally strong beckground field. In the weak field limit, it reduces to the BFKL equation, while in the general non-linear case it generates the evolution equations for eikonal-line operators previously derived by Balitsky and Kovchegov within perturbative QCD.

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“…where the overbar indicates interchange of symmetrization and antisymmetrization [15][16][17][18][19][20]. This formal expression links orthogonal groups acting on conventional bosonic tensor spaces to negative dimensional symplectic groups defined by their action on tensors in The group theory relation in (11) suggests that the SO(N ) model is mathematically similar to the theory with symmetry group…”

Section: /98mentioning

confidence: 99%

Misleading anomaly matchings?

1998

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We investigate the low energy dynamics of N = 1 supersymmetric SO(N ) gauge theories with a single symmetric tensor matter field. These theories exhibit non-trivial matching of global 't Hooft anomalies at the origin of moduli space. We argue that their quantum moduli spaces possess distinct Higgs and confining branches which touch at the origin in an interacting non-Abelian Coulomb phase. The matching of anomalies between microscopic degrees of freedom and colorless moduli therefore appears to be coincidental.We discuss a formal mathematical relation between the SO(N ) model and an analogous Sp(2N ) theory with a single antisymmetric matter field which provides an explanation for the anomaly matching coincidence. 2/98

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Random Magnetic Fields, Supersymmetry, and Negative Dimensions

Cited by 919 publications

References 13 publications

Confining membranes and dimensional reduction

Confining membranes and dimensional reduction

The renormalization group equation for the color glass condensate

Misleading anomaly matchings?

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