Loop calculations in quantum mechanical non-linear sigma models with fermions and applications to anomalies

Boer, Jan de; Peeters, Bas; Skenderis, Kostas; Nieuwenhuizen, P. van

doi:10.1016/0550-3213(95)00593-5

Cited by 60 publications

(83 citation statements)

References 70 publications

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“…Furthermore we showed in section 3 that for the N = 2 model mode regularization gives a non-covariant, susy-breaking counterterm Γ 2 /24, while both dimensional regularization and time slicing [19,31] give a vanishing counterterm. In MR, one may interpret the vanishing of N = 1 counterterm as due to the fact that this model is supersymmetric even off-shell (we have an equal number of bosonic and fermionic fields); and as a signal that such regularization scheme preserves the symmetry.…”

Section: Discussionmentioning

confidence: 89%

“…(2.10) This result can be compared with the one obtained employing other regularization schemes [31,18] that reads…”

Section: Flat Indicesmentioning

confidence: 97%

“…Its non covariant part was derived independently in [29] performing a change of coordinates (point canonical transformations) in the Hamiltonian in flat space. By carefully studying the relation between operator methods, discretized and continuous path integrals, the Feynman rules to be used in the continuum limit for Time Slicing were derived in [30], while the extensions to N = 1, 2 can be found in [31], where the N = 1, 2 TS counterterms are derived by Weyl ordering the supersymmetric Hamiltonians.…”

Section: Introductionmentioning

confidence: 99%

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Mode regularization forN= 1, 2 SUSY Sigma model

Bonezzi

Falconi

2008

J. High Energy Phys.

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Worldline N=1 and N=2 supersymmetric sigma models in curved background are useful to describe spin one-half and spin one particles coupled to external gravity, respectively. It is well known that worldline path integrals in curved space require regularization: we present here the mode-regularization for these models, finding in particular the corresponding counterterms, both in the case of flat and curved indices for worldline fermions. For N=1, using curved indices we find a contribution to the counterterm from the fermions that cancels the contribution of the bosons, leading to a vanishing total counterterm and thus preserving the covariance and supersymmetry of the classical action. Conversely in the case of N=2 supersymmetries we obtain a non-covariant counterterm with both curved and flat indices. This work completes the analysis of the known regularization schemes for N=1,2 nonlinear sigma models in one dimension.

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Section: Discussionmentioning

confidence: 89%

“…(2.10) This result can be compared with the one obtained employing other regularization schemes [31,18] that reads…”

Section: Flat Indicesmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mode regularization forN= 1, 2 SUSY Sigma model

Bonezzi

Falconi

2008

J. High Energy Phys.

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“…Since the Atiyah-Singer index theorem is related to the chiral anomaly, the methods used here can be looked upon as yet another derivation of the theorem, when the background is nongravitational. These anomalies were first formulated in terms of worldline pathintegrals in [35] and were put on more rigorous footing in [36] and the analysis finally culminated in a book [37]. One can compare the methods in these references with the methods here to appreciate the economy of arguments and calculational steps.…”

Section: Advances In High Energy Physicsmentioning

confidence: 99%

“…where we have taken thėcorrelator from [36] and used the fact that one-point functions vanish. Thus doing the integral in (55), one gets, upon using…”

Section: Propagator For the Spin-one Particlementioning

confidence: 99%

Worldline Path-Integral Representations for Standard Model Propagators and Effective Actions

Bhattacharya¹

2017

Advances in High Energy Physics

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We develop the formalism to do worldline calculations relevant for the Standard Model. For that, we first figure out the worldline representations for the free propagators of massless chiral fermions of a single generation and gauge bosons of the Standard Model. Then we extend the formalism to the massive and dressed cases for the fermions and compute the QED vertex. We then go over fermionic one-loop effective actions and anomalies. To our knowledge, in the places where there has been an attempt at deriving the gauge boson propagator, the derivation is somewhat contrived, and we believe our derivation is more straightforward. Moreover, our incorporation of internal degrees of freedom is novel and sports some new features. The derivation of the QED vertex is also new. The treatment of the fermionic one-loop effective actions leads to a particularly economical derivation of chiral anomalies and the gauge anomaly freedom in the Standard Model, improving upon the state of the art in the literature. The appropriate worldline formalism developed thus sets the stage for Standard Model calculations beyond the tree and one-loop cases that incorporate BernKosower type formulae for multiloop amplitudes, relevant for processes at the LHC.

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Quantum mechanical path integrals in curved spaces and the type-A trace anomaly

Bastianelli

Corradini

Vassura

2017

J. High Energ. Phys.

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Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in arbitrary coordinates is well understood, and known to require the use of a regularization scheme, in this article we take up an old proposal of constructing the path integral by using Riemann normal coordinates. The method assumes that curvature effects are taken care of by a scalar effective potential, so that the particle lagrangian is reduced to that of a linear sigma model interacting with the effective potential. After fixing the correct effective potential, we test the construction on spaces of maximal symmetry and use it to compute heat kernel coefficients and type-A trace anomalies for a scalar field in arbitrary dimensions up to d = 12. The results agree with expected ones, which are reproduced with great efficiency and extended to higher orders. We prove explicitly the validity of the simplified path integral on maximally symmetric spaces. This simplified path integral might be of further use in worldline applications, though its application on spaces of arbitrary geometry remains unclear.

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Loop calculations in quantum mechanical non-linear sigma models with fermions and applications to anomalies

Cited by 60 publications

References 70 publications

Mode regularization forN= 1, 2 SUSY Sigma model

Mode regularization forN= 1, 2 SUSY Sigma model

Worldline Path-Integral Representations for Standard Model Propagators and Effective Actions

Quantum mechanical path integrals in curved spaces and the type-A trace anomaly

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