Phase structure of self-dual lattice gauge theories in 4d

Anosova, Mariia; Gattringer, Christof; Iqbal, Nabil; Sulejmanpašić, Tin

doi:10.1007/jhep06(2022)149

Cited by 10 publications

(6 citation statements)

References 42 publications

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“…Note now that models of this sort can be coupled to both magnetic as well as electric matter in a standard way, just like in the space-time counterparts [4,9].…”

Section: Jhep05(2023)017mentioning

confidence: 99%

“…This is indeed what one expects in the continuum. 9 The story can be repeated for p-form gauge fields in arbitrary dimensions, where the two U(1) symmetries are p-form and the (D − p − 1)-form, with a mixed 't Hooft anomaly between them. Again one can show that two discrete subgroup Z N and Z M do not have a mixed anomalies only if GCD(N, M ) = 1.…”

Section: Jhep05(2023)017mentioning

confidence: 99%

“…(3.95) 9 In the continuum, one can put the background ZN gauge fields Ã for the ZN subgroup of the winding symmetry by the minimal coupling term 1 2π Ã ∧ dφ in the action. Now upon putting background ZM gauge field for the φ shift symmetry, the minimal coupling term becomes 1 2π Ã∧(dφ+A).…”

Section: Jhep05(2023)017mentioning

confidence: 99%

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Lattice quantum Villain Hamiltonians: compact scalars, U(1) gauge theories, fracton models and quantum Ising model dualities

Fazza

Sulejmanpašić

2023

J. High Energ. Phys.

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We construct Villain Hamiltonians for compact scalars and abelian gauge theories. The Villain integers are promoted to integral spectrum operators, whose canonical conjugates are naturally compact scalars. Further, depending on the theory, these conjugate operators can be interpreted as (higher-form) gauge fields. If a gauge symmetry is imposed on these dual gauge fields, a natural constraint on the Villain operator leads to the absence of defects (e.g. vortices, monopoles,…). These lattice models therefore have the same symmetry and anomaly structure as their corresponding continuum models. Moreover they can be formulated in a way that makes the well-know dualities look manifest, e.g. a compact scalar in 2d has a T-duality, in 3d is dual to a U(1) gauge theory, etc. We further discuss the gauged version of compact scalars on the lattice, its anomalies and solution, as well as a particular limit of the gauged XY model at strong coupling which reduces to the transverse-field Ising model. The construction for higher-form gauge theories is similar. We apply these ideas to the constructions of some models which are of interest to fracton physics, in particular the XY-plaquette model and the tensor gauge field model. The XY-plaquette model in 2+1d coupled to a tensor gauge fields at strong gauge coupling is also exactly described by a transverse field quantum J1 − J2 Ising model with J1 = 2J2, and discuss the phase structure of such models.

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“…Note now that models of this sort can be coupled to both magnetic as well as electric matter in a standard way, just like in the space-time counterparts [4,9].…”

Section: Jhep05(2023)017mentioning

confidence: 99%

Section: Jhep05(2023)017mentioning

confidence: 99%

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Lattice quantum Villain Hamiltonians: compact scalars, U(1) gauge theories, fracton models and quantum Ising model dualities

Fazza

Sulejmanpašić

2023

J. High Energ. Phys.

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“…In order to overcome this problem one may switch to a dual representation in terms of worldlines and worldsheets where the weight factors are real and positive. We do not discuss the derivation of this representation or the corresponding Monte Carlo techniques here, but refer to [13,14,15,23] for details.…”

Section: Pos(lattice2021)386mentioning

confidence: 99%

“…On the other hand, Villain's lattice action [8] is known to have better self-dual features, and the EM self-duality was initially discovered, not in the continuum but in specific lattice systems [9,10,11,12]. Yet it was noted only recently in [13,14,15], that a certain modification of Villain's action 4 can be used to construct models where magnetic and electric matter can be coupled on equal footing, and do not appear as artifacts of a theory. The gist of it is that such a formulation features both electric and magnetic gauge fields in the lattice action, which allows one to endow both electric and magnetic matter with spin, internal quantum numbers and arbitrary gauge charge, or to eliminate them all together, by setting the corresponding matter action to zero.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of self-dual U(1) lattice field theory with electric and magnetic matter

Anosova¹,

Gattringer²,

Iqbal³

et al. 2022

Proceedings of the 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)

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We study a recently proposed formulation of U(1) lattice field theory with electric and magnetic matter based on the Villain formulation. This discretization allows for a duality that gives rise to relations between weak and strong gauge coupling. There exists a self-dual value of the gauge coupling where one may study the model as a function of the remaining matter coupling. Using Monte Carlo simulations based on a worldline/worldsheet representation of the system we evaluate order parameters for spontaneous breaking of self-duality. We find that in some interval of the matter coupling self-duality becomes broken spontaneously. We determine the endpoints of this interval and study the nature of the corresponding critical points. Finally we explore the system away from the self-dual gauge coupling and show that when crossing the self-dual point a first order jump is seen in the order parameters.* Based on a parallel talk by M. Anosova.

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Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly

Hayashi

Tanizaki

2022

J. High Energ. Phys.

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We study properties of self-duality symmetry in the Cardy-Rabinovici model. The Cardy-Rabinovici model is the 4d U(1) gauge theory with electric and magnetic matters, and it enjoys the SL(2, ℤ) self-duality at low-energies. SL(2, ℤ) self-duality does not realize in a naive way, but we notice that the STp duality transformation becomes the legitimate duality operation by performing the gauging of ℤN 1-form symmetry with including the level-p discrete topological term. Due to such complications in its realization, the fusion rule of duality defects becomes a non-group-like structure, and thus the self-duality symmetry is realized as a non-invertible symmetry. Moreover, for some fixed points of the self-duality, the duality symmetry turns out to have a mixed gravitational anomaly detected on a K3 surface, and we can rule out the trivially gapped phase as a consequence of anomaly matching. We also uncover how the conjectured phase diagram of the Cardy-Rabinovici model satisfies this new anomaly matching condition.

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Phase structure of self-dual lattice gauge theories in 4d

Cited by 10 publications

References 42 publications

Lattice quantum Villain Hamiltonians: compact scalars, U(1) gauge theories, fracton models and quantum Ising model dualities

Lattice quantum Villain Hamiltonians: compact scalars, U(1) gauge theories, fracton models and quantum Ising model dualities

Numerical simulation of self-dual U(1) lattice field theory with electric and magnetic matter

Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly

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