Origins of global anomalies in quantum mechanics

Elitzur, Shmuel; Rabinovici, Eliezer; Frishman, Y.; Schwimmer, A.

doi:10.1016/0550-3213(86)90042-8

Cited by 64 publications

(88 citation statements)

References 7 publications

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“…III is a direct bosonic analogue of the results of Ref. 48 on global anomalies of fermions in 0 + 1 dimensions. In the context of SPT phases, our results in this paper also imply that the universal properties of an SPT phase can be captured by a much wider range of models than the NLSMs with spherical target space originally considered in Refs.…”

Section: Discussionmentioning

confidence: 99%

“…are equivalent to one-dimensional Dirac operators for a fermion in one spacetime dimension coupled to the external field A = A t dt [48]. As we discussed in Appendix B, the overall sign of these Pfaffians is ambiguous, since we are free to alter the order of factors in the definition of the path integral measure.…”

Section: Boundary Partition Function and Global Anomaly For All Tamentioning

confidence: 99%

“…The BTI state in two dimensions has the symmetry group G = U (1) ⋊ Z 2 , where Z 2 represents a unitary charge-conjugation symmetry. Our exact computation of the boundary partition function shows that the boundary of the BTI does indeed exhibit a bosonic analogue of the global anomaly of Dirac fermions in 0 + 1 dimensions which also have U (1) symmetry and Z 2 chargeconjugation symmetry [48]. We first compute this anomaly within the O(3) NLSM description (with target space S 2 ) of the BTI boundary which we previously used in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Perturbative and global anomalies in bosonic analogs of integer quantum Hall and topological insulator phases

Lapa

Hughes

2017

Phys. Rev. B

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We study perturbative and global anomalies at the boundaries of bosonic analogues of integer quantum Hall (BIQH) and topological insulator (BTI) phases using a description of the boundaries of these phases in terms of a nonlinear sigma model (NLSM) with Wess-Zumino term. One of the main results of the paper is that these anomalies are robust against arbitrary smooth deformations of the target space of the NLSM which describes the phase, provided that the deformations also respect the symmetry of the phase. In the first part of the paper we discuss the perturbative U (1) anomaly at the boundary of BIQH states in all odd (spacetime) dimensions. In the second part we study global anomalies at the boundary of BTI states in even dimensions. In a previous work [Phys. Rev. B 95, 035149 (2017)] we argued that the boundary of the BTI phase exhibits a global anomaly which is an analogue of the parity anomaly of Dirac fermions in three dimensions. Here we elevate this argument to a proof for the boundary of the two-dimensional BTI state by explicitly computing the partition function of the gauged NLSM describing the boundary. We then use the powerful equivariant localization technique to show that this global anomaly is robust against all smooth deformations of the target space of the NLSM which preserve the U (1) ⋊ Z2 symmetry of the BTI state. We also comment on the difficulties of generalizing this latter proof to higher dimensions. Finally, we discuss the expected low energy behavior of the boundary theories studied in this paper when the coupling constants are allowed to flow under the renormalization group.

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Section: Discussionmentioning

confidence: 99%

Section: Boundary Partition Function and Global Anomaly For All Tamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Perturbative and global anomalies in bosonic analogs of integer quantum Hall and topological insulator phases

Lapa

Hughes

2017

Phys. Rev. B

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“…A curiosity of this 4D case is that there is also a U(1) "spin-shell" constraint that has no direct relation to spin. One might be concerned about the possibility of a global U(1) anomaly due to the "worldline fermions" [10,33] but there is no anomaly here because the number of fermi oscillators is even.…”

Section: Jhep06(2017)151mentioning

confidence: 99%

Pauli-Lubanski, supertwistors, and the superspinning particle

Arvanitakis

Mezincescu

Townsend

2017

J. High Energ. Phys.

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We present a novel construction of the super-Pauli-Lubanski pseudo-vector for 4D supersymmetry and show how it arises naturally from the spin-shell constraints in the supertwistor formulation of superparticle dynamics. We illustrate this result in the context of a simple classical action for a "superspinning particle" of superspin 1/2. We then use an Sl(2; K)-spinor formalism for K = R, C, H to unify our 4D results with previous results for 3D and 6D.

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“…We find that when c 1 = c 2 , c 3 = c 4 and c i = 0, the effective Lagrangian is surprisingly simplified, and is given by 1 2 sign(b)(b+a 0 ) (where we have turned on the background a 0 for gauge field A 0 ), completely independent of the backgrounds c i . The resulting effective Lagrangian is anomalous under the global gauge transformation [19,20], but is invariant under b → −b, a 0 → −a 0 transformation which corresponds to the charge conjugation invariance [19]. One can restore the invariance under the large gauge transformation by adding bare Chern-Simons (CS) terms of the form − We find the resulting potential in M(atrix) theory is independent of the backgrounds c i related to the angles between two D4-branes (after T-dualities).…”

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confidence: 99%

Creation of fundamental string inM(atrix)theory

1998

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The potential between two D4-branes at angles with partially unbroken supersymmetry is computed, and is used to discuss the creation of a fundamental string when two such D4-branes cross each other in M(atrix) theory. The effective Lagrangian is shown to be anomalous at 1-loop approximation, but it can be modified by bare Chern-Simons terms to preserve the invariance under the large gauge transformation. The resulting effective potential agrees with that obtained from the string calculations. The result shows that a fundamental string is created in order to cancel the repulsive force between two D4-branes at proper angles. * ohta@phys.wani.osaka-u.ac.jp † simtak@phys.wani.osaka-u.ac.jp ‡ jgzhou@phys.wani.osaka-u.ac.jp, JSPS postdoctral fellowRecently the creation of a fundamental string when a D0-brane crosses a D8-brane in type IIA theory, and the creation of a longitudinal membrane in M-theory when two longitudinal M5-branes cross each other, have been studied from various points of view [1][2][3][4][5][6][7].In the string theory context, by requiring RR charge conservation, it was first found in [1] that a third brane is created when two certain branes cross. In [2], the anomaly equation was exploited to show that when the two branes in question cross each other an energy level crosses zero and a single particle or hole is created, and this was interpreted as the creation of an open string or brane. It was also suggested that the induced charge on the D8-brane worldvolume indicates the creation of a string when the D0-brane crosses the D8-brane [3]. The one-loop open string calculation in ref. [4] revealed that the potential of the D0-D8 system vanishes due to the cancellation of the forces coming from the dilatongraviton exchange and a fundamental string created when two such branes cross.On the other hand, more and more evidence has accumulated to show that M-theory could be described in terms of a matrix model -M(atrix) theory [8]. Many consistency checks have been done, including the calculation of potentials between various D-branes [9][10][11][12][13][14]. It is then natural to study the brane creation in the context of M(atrix) theory, but only a few papers discuss this phenomenon. The authors of ref. [6] argued that the effective potential between two M5-branes is dominated by the contribution from the chiral fermionic zero mode in the off-diagonal degrees of freedom. On the other hand, ref. [13] calculated the effective potential between D0-and D8-branes, with the approximation of small b and c i (b is the distance between D0-and D8-branes along X 9 , and c i 's stand for backgrounds). Since the effective potential is computed only for small b and c i , it is hard

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Origins of global anomalies in quantum mechanics

Cited by 64 publications

References 7 publications

Perturbative and global anomalies in bosonic analogs of integer quantum Hall and topological insulator phases

Perturbative and global anomalies in bosonic analogs of integer quantum Hall and topological insulator phases

Pauli-Lubanski, supertwistors, and the superspinning particle

Creation of fundamental string inM(atrix)theory

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