Free energy and defect C-theorem in free fermion

Sato, Yoshiki

doi:10.1007/jhep05(2021)202

Cited by 18 publications

(10 citation statements)

References 58 publications

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“…For example, unlike standard d = 2 CFTs where there is a single central charge c, p = 2 dCFTs have three trace anomaly coefficients labelled b, d 1 , and d 2 , which play the role of putative central charges. 1 The absence of a conserved stress tensor makes proving statements about positivity [12] and c-theorems [13][14][15][16][17][18] for defect central charges more difficult, though not impossible. This is particularly salient for p = 2 where one does not generally expect an enhancement from a global SO(2, 2) conformal symmetry to a full Virasoro symmetry unless the defect completely decouples or the ambient theory is topological.…”

Section: Jhep08(2021)013mentioning

confidence: 99%

Monodromy defects in free field theories

Bianchi

Chalabi

Prochazka

et al. 2021

J. High Energ. Phys.

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We study co-dimension two monodromy defects in theories of conformally coupled scalars and free Dirac fermions in arbitrary d dimensions. We characterise this family of conformal defects by computing the one-point functions of the stress-tensor and conserved current for Abelian flavour symmetries as well as two-point functions of the displacement operator. In the case of d = 4, the normalisation of these correlation functions are related to defect Weyl anomaly coefficients, and thus provide crucial information about the defect conformal field theory. We provide explicit checks on the values of the defect central charges by calculating the universal part of the defect contribution to entanglement entropy, and further, we use our results to extract the universal part of the vacuum Rényi entropy. Moreover, we leverage the non-supersymmetric free field results to compute a novel defect Weyl anomaly coefficient in a d = 4 theory of free $$ \mathcal{N} $$ N = 2 hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free d = 4 Maxwell theory and show that their central charges vanish.

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Section: Jhep08(2021)013mentioning

confidence: 99%

Monodromy defects in free field theories

Bianchi

Chalabi

Prochazka

et al. 2021

J. High Energ. Phys.

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show abstract

“…( 6. 15) is defined at an arbitrary UV cut-off scale Λ, which we can interpret as the defect thickness. The IR physics should be independent of this scale and eventually we will send Λ → ∞.…”

Section: Defect Beta Functionmentioning

confidence: 99%

“…For example, unlike standard d = 2 CFTs where there is a single central charge c, p = 2 dCFTs have three trace anomaly coefficients labelled b, d 1 , and d 2 , which play the role of putative central charges. 1 The absence of a conserved stress tensor makes proving statements about positivity [12] and c-theorems [13][14][15][16][17] for defect central charges more difficult, though not impossible. This is particularly salient for p = 2 where one does not generally expect an enhancement from a global SO(2, 2) conformal symmetry to a full Virasoro symmetry unless the defect completely decouples or the ambient theory is topological.…”

mentioning

confidence: 99%

Monodromy Defects in Free Field Theories

Bianchi,

Chalabi,

Procházka

et al. 2021

Preprint

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We study co-dimension two monodromy defects in theories of conformally coupled scalars and free Dirac fermions in arbitrary d dimensions. We characterise this family of conformal defects by computing the one-point functions of the stress-tensor and conserved current for Abelian flavour symmetries as well as two-point functions of the displacement operator. In the case of d = 4, the normalisation of these correlation functions are related to defect Weyl anomaly coefficients, and thus provide crucial information about the defect conformal field theory. We provide explicit checks on the values of the defect central charges by calculating the universal part of the defect contribution to entanglement entropy, and further, we use our results to extract the universal part of the vacuum Rényi entropy. Moreover, we leverage the non-supersymmetric free field results to compute a novel defect Weyl anomaly coefficient in a d = 4 theory of free N = 2 hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free d = 4 Maxwell theory and show that their central charges vanish.

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“…Therefore we obtain the partition function of the massless Dirac fermion on S a × AdS b which has the same expression as we obtained it for S a+b in (4.7). In the recent work of [31] the equality of the partition function of Dirac fermion has been checked numerically.…”

Section: Jhep10(2021)236mentioning

confidence: 99%

Partition functions of higher derivative conformal fields on conformally related spaces

Mukherjee

2021

J. High Energ. Phys.

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The character integral representation of one loop partition functions is useful to establish the relation between partition functions of conformal fields on Weyl equivalent spaces. The Euclidean space Sa × AdSb can be mapped to Sa+b provided Sa and AdSb are of the same radius. As an example, to begin with, we show that the partition function in the character integral representation of conformally coupled free scalars and fermions are identical on Sa × AdSb and Sa+b. We then demonstrate that the partition function of higher derivative conformal scalars and fermions are also the same on hyperbolic cylinders and branched spheres. The partition function of the four-derivative conformal vector gauge field on the branched sphere in d = 6 dimension can be expressed as an integral over ‘naive’ bulk and ‘naive’ edge characters. However, the partition function of the conformal vector gauge field on $$ {S}_q^1 $$ S q 1 × AdS5 contains only the ‘naive’ bulk part of the partition function. This follows the same pattern which was observed for the partition of conformal p-form fields on hyperbolic cylinders. We use the partition function of higher derivative conformal fields on hyperbolic cylinders to obtain a linear relationship between the Hofman-Maldacena variables which enables us to show that these theories are non-unitary.

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Free energy and defect C-theorem in free fermion

Cited by 18 publications

References 58 publications

Monodromy defects in free field theories

Monodromy defects in free field theories

Monodromy Defects in Free Field Theories

Partition functions of higher derivative conformal fields on conformally related spaces

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