Fermionization and boundary states in 1+1 dimensions

Fukusumi, Yoshiki; Tachikawa, Yuji; Zheng, Yunqin

doi:10.21468/scipostphys.11.4.082

Cited by 25 publications

(23 citation statements)

References 59 publications

(108 reference statements)

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“…The authors are grateful to Yoshiki Fukusumi, Rohit Kalloor, Ryohei Kobayashi, Yuji Tachikawa, and Yunqin Zheng for discussions. We also thank Yoshiki Fukusumi, Yuji Tachikawa, and Yunqin Zheng for collaborations at the early stages of the work, and for the coordination of the publication of [35] with the present paper. We also especially thank Rohit Kalloor for detailed discussions and…”

Section: Acknowledgementsmentioning

confidence: 99%

“…The paper also lists all the fermionic minimal models with holomorphic parity symmetry, but this is beyond the scope of the present paper. We also like to mention another paper [35] by Yoshiki Fukusumi, Yuji Tachikawa, and Yunqin Zheng, with whom we discussed together in the early stages of both work. We also coordinated the publication of the two.…”

Section: Introductionmentioning

confidence: 99%

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Fermionization of conformal boundary states

Ebisu,

Watanabe

2021

Preprint

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We construct the complete set of boundary states of two-dimensional fermionic CFTs using that of the bosonic counterpart. We see that there are two groups of boundary conditions, which contributes to the open-string partition function by characters with integer coefficients, or with √ 2 times integer coefficients. We argue that, using the argument of [1], this √ 2 indicates a single unpaired Majorana zero mode, and that these two groups of boundary conditions are mutually incompatible.

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Section: Acknowledgementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fermionization of conformal boundary states

Ebisu,

Watanabe

2021

Preprint

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“…This latter manipulation is called fermionization, and for minimal models it was studied by Petkova already in the eighties, see [68,69]. More recently, it has been attracting interest [63,[70][71][72][73][74][75] in the context…”

Section: Fermionization Of Integrable Field Theoriesmentioning

confidence: 99%

Crosscap States in Integrable Field Theories and Spin Chains

Caetano,

Komatsu

2021

Preprint

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We study crosscap states in integrable field theories and spin chains in 1 + 1 dimensions. We derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. We then compute the crosscap entropy, i.e. the overlap for the ground state, in some examples. In the examples we analyzed, the result turns out to decrease monotonically along the renormalization group flow except in cases where the discrete symmetry is spontaneously broken in the infrared. We next introduce crosscap states in integrable spin chains, and obtain determinant expressions for the overlaps with energy eigenstates. These states are long-range entangled and their entanglement entropy grows linearly until the size of the subregion reaches half the system size. This property is reminiscent of pure-state black holes in holography and makes them interesting for use as initial conditions of quantum quench. As side results, we propose a generalization of Zamolodchikov's staircase model to flows between D-series minimal models, and discuss the relation to fermionic minimal models and the GSO projection.

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“…Let us note that fermionic theories in principle can always be studied in terms of corresponding bosonic theories via bosonization/fermionization map [27][28][29][30][31][32][33][34]. It however becomes more subtle to distinguish fermionic theories with different anomalies of the global symmetries after the bosonization.…”

Section: Introductionmentioning

confidence: 99%

Spin-cobordisms, surgeries and fermionic modular bootstrap

Grigoletto¹,

Putrov²

2021

Preprint

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We consider general fermionic quantum field theories with a global finite group symmetry G, focusing on the case of 2-dimensions and torus spacetime. The modular transformation properties of the family of partition functions with different backgrounds is determined by the 't Hooft anomaly of G and fermion parity. For a general possibly non-abelian G we provide a method to determine the modular transformations directly from the bulk 3d invertible topological quantum field theory (iTQFT) corresponding to the anomaly by inflow. We also describe a method of evaluating the character map from the real representation ring of G to the group which classifies anomalies. Physically the value of the map is given by the anomaly of free fermions in a given representation. We assume classification of the anomalies/iTQFTs by spin-cobordisms. As a byproduct, for all abelian symmetry groups G, we provide explicit combinatorial expressions for corresponding spin-bordism invariants in terms of surgery representation of arbitrary closed spin 3-manifolds. We work out the case of G = Z 2 in detail, and, as an application, we consider the constraints that 't Hooft anomaly puts on the spectrum of the infrared conformal field theory.

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Fermionization and boundary states in 1+1 dimensions

Cited by 25 publications

References 59 publications

Fermionization of conformal boundary states

Fermionization of conformal boundary states

Crosscap States in Integrable Field Theories and Spin Chains

Spin-cobordisms, surgeries and fermionic modular bootstrap

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