PT-Symmetric Quantum Field Theory

Bender, Carl M.; Simos, Theodore E.; Psihoyios, George; Tsitouras, Ch.; Anastassi, Zacharias

doi:10.1063/1.3636813

Cited by 20 publications

(33 citation statements)

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“…Therefore we expect γ k = O(g 2 ) for k ≤ n−1. With this condition one can solve the recurrence relation to obtain 24) which is in perfect agreement with the perturbative result [10]. Note that in the case n = 2 we correctly reproduce eq.…”

Section: Jhep04(2017)127supporting

confidence: 72%

“…Invariance under this symmetry implies the Z 2 parity of the previous section as a special case for all even potentials, but extends the possible symmetry to incorporate odd potentials, provided that the latter have a purely imaginary critical coupling g. It has been argued that P T -symmetry is a valid symmetry, in the sense that it suffices to ensure the stability of the corresponding theory [23][24][25] and to have a spectrum bounded from below. On the more pragmatic side, it has been argued that these models interpolate with a well known sequence of minimal non-unitary multicritical models which begins with the Lee-Yang universality class [14].…”

Section: Jhep04(2017)127mentioning

confidence: 80%

“…These odd potentials seem to be protected by a generalization of parity that has been linked to P T -symmetry [23][24][25]. This manifests in the fact that for all the n > 1 models one has leading negative γ 1 and γ 2 anomalous dimensions (the latter is positive in the Lee-Yang universality class).…”

Section: Jhep04(2017)127mentioning

confidence: 99%

“…The odd potentials are not invariant under parity, but are instead protected by a generalization of parity, which has been related to P T -symmetry [23][24][25]. On a general action S[φ] as in (1.1) P T -symmetry acts as…”

Section: Jhep04(2017)127mentioning

confidence: 99%

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Leading CFT constraints on multi-critical models in d > 2

Codello

Safari

Vacca

et al. 2017

J. High Energ. Phys.

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Abstract:We consider the family of renormalizable scalar QFTs with self-interacting potentials of highest monomial φ m below their upper critical dimensions d c = 2m m−2 , and study them using a combination of CFT constraints, Schwinger-Dyson equation and the free theory behavior at the upper critical dimension. For even integers m ≥ 4 these theories coincide with the Landau-Ginzburg description of multi-critical phenomena and interpolate with the unitary minimal models in d = 2, while for odd m the theories are non-unitary and start at m = 3 with the Lee-Yang universality class. For all the even potentials and for the Lee-Yang universality class, we show how the assumption of conformal invariance is enough to compute the scaling dimensions of the local operators φ k and of some families of structure constants in either the coupling's or the -expansion. For all other odd potentials we express some scaling dimensions and structure constants in the coupling's expansion.

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Section: Jhep04(2017)127supporting

confidence: 72%

Section: Jhep04(2017)127mentioning

confidence: 80%

Section: Jhep04(2017)127mentioning

confidence: 99%

Section: Jhep04(2017)127mentioning

confidence: 99%

See 2 more Smart Citations

Leading CFT constraints on multi-critical models in d > 2

Codello

Safari

Vacca

et al. 2017

J. High Energ. Phys.

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“…[30] and [31]. Subsequently, the gauge interactions are introduced and the tree-level properties of the model are described.…”

Section: Jhep11(2015)111mentioning

confidence: 99%

Non-Hermitian extension of gauge theories and implications for neutrino physics

Alexandre

Bender

Millington

2015

J. High Energ. Phys.

Self Cite

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An extension of QED is considered in which the Dirac fermion has both Hermitian and anti-Hermitian mass terms, as well as both vector and axial-vector couplings to the gauge field. Gauge invariance is restored when the Hermitian and anti-Hermitian masses are of equal magnitude, and the theory reduces to that of a single massless Weyl fermion. An analogous non-Hermitian Yukawa theory is considered, and it is shown that this model can explain the smallness of the light-neutrino masses and provide an additional source of leptonic CP violation.

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‐symmetry and Schrödinger operators. The double well case

Mecherout

Boussekkine

Ramond

et al. 2015

Mathematische Nachrichten

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We study a class of PT -symmetric semiclassical Schrödinger operators, which are perturbations of a selfadjoint one. Here, we treat the case where the unperturbed operator has a double-well potential. In the simple well case, two of the authors have proved in [6] that, when the potential is analytic, the eigenvalues stay real for a perturbation of size O(1). We show here, in the double-well case, that the eigenvalues stay real only for exponentially small perturbations, then bifurcate into the complex domain when the perturbation increases and we get precise asymptotic expansions. The proof uses complex WKB-analysis, leading to a fairly explicit quantization condition.

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PT-Symmetric Quantum Field Theory

Cited by 20 publications

References 0 publications

Leading CFT constraints on multi-critical models in d > 2

Leading CFT constraints on multi-critical models in d > 2

Non-Hermitian extension of gauge theories and implications for neutrino physics

‐symmetry and Schrödinger operators. The double well case

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