Quantum field theory of non-abelian strings and vortices

Alford, Mark; Lee, Kai-Ming; March-Russell, John; Preskill, John

doi:10.1016/0550-3213(92)90468-q

Cited by 104 publications

(140 citation statements)

References 39 publications

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“…The former occurs in models of p-wave superconductors as well 23 . Field theories with such non-abelian statistics also have been found 24,25,26 . In a number of these cases, the long-distance physics can be described by a Chern-Simons gauge theory, which breaks time-reversal symmetry.…”

Section: Introductionmentioning

confidence: 90%

Realizing non-Abelian statistics in time-reversal-invariant systems

2005

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We construct a series of 2+1-dimensional models whose quasiparticles obey non-Abelian statistics. The adiabatic transport of quasiparticles is described by using a correspondence between the braid matrix of the particles and the scattering matrix of 1+1-dimensional field theories. We discuss in depth lattice and continuum models whose braiding is that of SO(3) Chern-Simons gauge theory, including the simplest type of non-Abelian statistics, involving just one type of quasiparticle. The ground-state wave function of an SO(3) model is related to a loop description of the classical twodimensional Potts model. We discuss the transition from a topological phase to a conventionallyordered phase, showing in some cases there is a quantum critical point.

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Section: Introductionmentioning

confidence: 90%

Realizing non-Abelian statistics in time-reversal-invariant systems

2005

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“…In general, there are many kinds of loop braiding processes we can consider -including processes involving two loops [41][42][43] , three loops [24][25][26]44,45 , or even more complicated configurations. Here, we will follow Ref.…”

Section: Excitations and Three-loop Braiding Statisticsmentioning

confidence: 99%

Topological invariants for gauge theories and symmetry-protected topological phases

2015

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We study the braiding statistics of particle-like and loop-like excitations in 2D and 3D gauge theories with finite, Abelian gauge group. The gauge theories that we consider are obtained by gauging the symmetry of gapped, short-range entangled, lattice boson models. We define a set of quantities -called topological invariants -that summarize some of the most important parts of the braiding statistics data for these systems. Conveniently, these invariants are always Abelian phases, even if the gauge theory supports excitations with non-Abelian statistics. We compute these invariants for gauge theories obtained from the exactly soluble group cohomology models of Chen, Gu, Liu and Wen, and we derive two results. First, we find that the invariants take different values for every group cohomology model with finite, Abelian symmetry group. Second, we find that these models exhaust all possible values for the invariants in the 2D case, and we give some evidence for this in the 3D case. The first result implies that every one of these models belongs to a distinct SPT phase, while the second result suggests that these models may realize all SPT phases. These results support the group cohomology classification conjecture for SPT phases in the case where the symmetry group is finite, Abelian, and unitary.

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“…In such cases, junctions may form at which three different strings meet. Such junctions can also appear in networks of 'non-Abelian strings', for which the fundamental group π 1 (M) of the manifold of degenerate vacua, which classifies the strings, is non-Abelian [10,11]. Several papers have considered the evolution of networks of strings with junctions [12,13,14,15], in particular the question of whether such a network would evolve to a scaling regime as expected for an ordinary cosmic-string network [16].…”

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confidence: 99%

Collisions of Strings with Y Junctions

2006

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We study the dynamics of Nambu-Goto strings with junctions at which three strings meet. In particular, we exhibit one simple exact solution and examine the process of intercommuting of two straight strings, in which they exchange partners but become joined by a third string. We show that there are important kinematical constraints on this process. The exchange cannot occur if the strings meet with very large relative velocity. This may have important implications for the evolution of cosmic superstring networks and non-abelian string networks.There has been renewed interest in cosmic strings, both because of tentative observational evidence [1,2] and because they appear to arise naturally in scenarios based on string theory [3,4,5], as well as in field theories [6,7]. Although the recent close inspection by the Hubble Space Telescope of the area of interest in [1, 2] appears to indicate that no string is present [8], the possibility remains that strings may be found through other types of observation in the Universe. Moreover, in the scenarios based on string theory, several different kinds of cosmic strings may appear, in particular F-and D-strings and (p, q) composites, formed of p F-strings and q D-strings [9]. In such cases, junctions may form at which three different strings meet. Such junctions can also appear in networks of 'non-Abelian strings', for which the fundamental group π 1 (M) of the manifold of degenerate vacua, which classifies the strings, is non-Abelian [10,11]. Several papers have considered the evolution of networks of strings with junctions [12,13,14,15], in particular the question of whether such a network would evolve to a scaling regime as expected for an ordinary cosmic-string network [16].In this paper, we study the dynamics of three-string junctions in a local-string network, that is to say one where the individual strings have no long-range interactions and are well described by the Nambu-Goto action. Our approach is similar to the one adopted by 't Hooft in Ref. [17], in which he represented baryons as pieces of open string connected at one common point. However, our method differs from his in significant ways. In particular, our treatment applies to strings with different tensions, and we use a temporal world-sheet coordinate equal to the global time. For ordinary cosmic strings, the existence of exact solutions for oscillating string loops [18,19] was important in analyzing the likely behavior of loops in general, and some exact solutions are also known for open strings with junctions. Here we give one very simple example of an exact solution, but our main focus is on the question of what happens when two strings cross.When two ordinary cosmic strings intersect they normally 'intercommute', or exchange partners [20,21,22,23,24]. But for the strings we are considering this is generally impossible. What we expect instead is that the strings will become joined by a third string. The dynamical problem of finding the intercommuting probability for junction-forming strings has been dis...

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Quantum field theory of non-abelian strings and vortices

Cited by 104 publications

References 39 publications

Realizing non-Abelian statistics in time-reversal-invariant systems

Realizing non-Abelian statistics in time-reversal-invariant systems

Topological invariants for gauge theories and symmetry-protected topological phases

Collisions of Strings with Y Junctions

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