String representation of Abelian Higgs theory and Aharonov-Bohm effect on the lattice

Polikarpov, M.I.; Wiese, U.‐J.; Zubkov, M. A.

doi:10.1016/0370-2693(93)91516-p

Cited by 73 publications

(68 citation statements)

References 15 publications

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“…It has also recently been exploited in dual models of cosmic strings [7], and axionic black hole theories [8] where the axion charge is physically detectable only by external cosmic strings in a 4 dimensional Aharanov-Bohm type process [9] identical to what we shall consider here. These 4 dimensional Aharanov-Bohm phases also appear in field theories of the QCD string [10].…”

Section: Introductionmentioning

confidence: 81%

Canonical BF-type topological field theory and fractional statistics of strings

Bergeron

Semenoff²,

Szabo³

1995

Nuclear Physics B

104

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We consider BF-type topological field theory coupled to non-dynamical particle and string sources on spacetime manifolds of the form IR 1 × M 3 , where M 3 is a 3-manifold without boundary. Canonical quantization of the theory is carried out in the Hamiltonian formalism and explicit solutions of the Schrödinger equation are obtained. We show that the Hilbert space is finite dimensional and the physical states carry a one-dimensional projective representation of the local gauge symmetries. When M 3 is homologically nontrivial the wavefunctions in addition carry a multi-dimensional projective representation, in terms of the linking matrix of the homology cycles of M 3 , of the discrete group of large gauge transformations. The wavefunctions also carry a one-dimensional representation of the non-trivial linking of the particle trajectories and string surfaces in M 3 . This topological field theory therefore provides a phenomenological generalization of anyons to (3 + 1) dimensions where the holonomies representing fractional statistics arise from the adiabatic transport of particles around strings. We also discuss a duality between large gauge transformations and these linking operations around the homology cycles of M 3 , and show that this canonical quantum field theory provides novel quantum representations of the cohomology of M 3 and its associated motion group. *

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Section: Introductionmentioning

confidence: 81%

Canonical BF-type topological field theory and fractional statistics of strings

Bergeron

Semenoff²,

Szabo³

1995

Nuclear Physics B

104

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“…It can be derived without extra assumptions [9] for the confining phase of compact U (1) gauge theories [10]. The resulting strings are dual versions of the magnetic strings of the Abelian Higgs model [11,12]. Moreover, the action is a specific form of an earlier-proposed class of actions which would generate surfaces with non-trivial elastic properties [13].…”

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confidence: 99%

Strings with Negative Stiffness and Hyperfine Structure

1999

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We propose a new string model by adding a higher-order gradient term to the rigid string, so that the stiffness can be positive or negative without loosing stability. In the large-D approximation, the model has three phases, one of which with a new type of generalized "antiferromagnetic" orientational correlations. We find an infrared-stable fixed point describing world-sheets with vanishing tension and Hausdorff dimension DH = 2. Crumpling is prevented by the new term which suppresses configurations with rapidly changing extrinsic curvature.PACS: 11.25.Pm 1. So far, fundamental strings [1] can be quantized only in critical spacetime dimensions D c , due to the difficulty of handling the Liouville field, which does not decouple in dimensions different from D c . Strings in four space-time dimensions, however, are of great physical importance since they are supposed to describe the confining phase of non-Abelian gauge theories [2], as confirmed by recent precision numerical tests [3]. As yet, there exists no consistent quantum theory of such strings. Attempts in this direction based on discrete models for the Liouville field failed [4], since these could not be generalized beyond one dimension. Further hope was based on strings with extrinsic curvature stiffness [5], but the infrared irrelevance of stiffness did not prevent the worldsheets from crumpling [6].Recent progress in this field is based on a new type of action. In its local formulation [7], the string action is induced by an antisymmetric tensor field. This action realizes explicitly the necessary zig-zag invariance of confining strings [8]. It can be derived without extra assumptions [9] for the confining phase of compact U (1) gauge theories [10]. The resulting strings are dual versions of the magnetic strings of the Abelian Higgs model [11,12]. Moreover, the action is a specific form of an earlier-proposed class of actions which would generate surfaces with non-trivial elastic properties [13].The characteristic of the effective string action obtained by integrating out the tensor field is a non-local interaction with negative stiffness between world-sheet elements. Such an interaction has been shown [14] to produce the correct high-temperature behavior of confining strings known from large-N QCD calculations [15].Moreover, it has been proposed [16] as a mechanism leading to smooth strings, with "long-range" orientational correlations, a fact confirmed by recent numerical simulations [17].In this letter we report on further progress in this field by considering the simplest possible model in this class of actions, obtained by adding to the rigid string the nextorder gradient term. The new model is defined in euclidean space by the actionwhere D a are covariant derivatives with respect to the induced metric g ab = ∂ a x µ ∂ b x µ on the surface x (ξ 0 , ξ 1 ) and we have used units c = 1,h = 1. Here, the bracket has to be considered as representing the first few terms in the expansion of the non-local interaction mediated by the original antisymmetric ...

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“…Notice that, for the special periodic value θ = π of the vacuum angle, when the geometry of the string worldsheets is such that their deRham currents are self-dual 2-forms, the sum over intersection numbers in (3.38) vanishes and we are left with a pure effective string theory (plus an additional non-local particle-string Aharonov-Bohm interaction [17,19]). This is precisely the value of θ that was found in [32] to be induced by the dynamical cancellation of folded string configurations.…”

Section: Effective String Theorymentioning

confidence: 99%

“…In abelian Higgs field theories, where the charged particles are represented by dynamical scalar fields, the structures described in section 3 emerge as the leading orders of a large Higgs mass expansion. The present formalism, which involves non-dynamical point particles, naturally incorporates the particle-string Aharonov-Bohm phases [17,19], extrinsic curvature terms [18,19], and similar long-range string intersection interactions [19] that have been discussed extensively in Higgs models. The emergence of smooth surface invariants in this topological field theory is intriguing in light of recent work [40] on observables in nonabelian BF theories which suggests that surface observables yield possibly new invariants of immersed surfaces in 4-manifolds.…”

Section: Transformation Properties Of the Physical Statesmentioning

confidence: 99%

String holonomy and extrinsic geometry in four-dimensional topological gauge theory

Szabo¹

1998

Nuclear Physics B

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The most general gauge-invariant marginal deformation of four-dimensional abelian BF -type topological field theory is studied. It is shown that the deformed quantum field theory is topological and that its observables compute, in addition to the usual linking numbers, smooth intersection indices of immersed surfaces which are related to the Euler and Chern characteristic classes of their normal bundles in the underlying spacetime manifold. Canonical quantization of the theory coupled to non-dynamical particle and string sources is carried out in the Hamiltonian formalism and explicit solutions of the Schrödinger equation are obtained. The wavefunctions carry a one-dimensional unitary representation of the particle-string exchange holonomies and of non-topological stringstring intersection holonomies given by adiabatic limits of the worldsheet Euler numbers. They also carry a multi-dimensional projective representation of the deRham complex of the underlying spatial manifold and define a generalization of the presentation of its motion group from Euclidean space to an arbitrary 3-manifold. Some potential physical applications of the topological field theory as a dual model for effective vortex strings are discussed.

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String representation of Abelian Higgs theory and Aharonov-Bohm effect on the lattice

Cited by 73 publications

References 15 publications

Canonical BF-type topological field theory and fractional statistics of strings

Canonical BF-type topological field theory and fractional statistics of strings

Strings with Negative Stiffness and Hyperfine Structure

String holonomy and extrinsic geometry in four-dimensional topological gauge theory

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