Path-integral formulation of conformal anomalies

Shizuya, K.; Tsukahara, H.

doi:10.1007/bf01551077

Cited by 12 publications

(9 citation statements)

References 10 publications

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“…with τ → 0 + in Γ at the very end. This choice Γ = e τ D 2 of the ultraviolet regulator is manifestly supersymmetric and is a natural one [10,16] that controls quantum fluctuations within the background-field method. To evaluate Eq.…”

Section: Anomaliesmentioning

confidence: 99%

“…In Fujikawa's path-integral formulation of anomalies [14,15] all known anomalies arise from regularized Jacobian factors which take precisely the form (fields)×(equations of motion). We shall therefore avoid using the equations of motion in our analysis and keep track of the potentially anomalous products such as X µ ; actually, conformal [16] and superconformal [17] anomalies in four dimensions were studied along this line earlier.…”

Section: Superfield Supercurrentmentioning

confidence: 99%

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Superfield formulation of central charge anomalies in two-dimensional supersymmetric theories with solitons

Shizuya

2004

Phys. Rev. D

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A superfield formulation is presented of the central charge anomaly in quantum corrections to solitons in two-dimensional theories with N = 1 supersymmetry. Extensive use is made of the superfield supercurrent, that places the supercurrent J µ α , energy-momentum tensor Θ µν and topological current ζ µ in a supermultiplet, to study the structure of supersymmetry and related superconformal symmetry in the presence of solitons. It is shown that the supermultiplet structure of (J µ α , Θ µν , ζ µ ) is kept exact while the topological current ζ µ acquires a quantum modification through the superconformal anomaly. In addition, the one-loop superfield effective action is explicitly constructed to verify the BPS saturation of the soliton spectrum as well as the effect of the anomaly.

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Section: Anomaliesmentioning

confidence: 99%

Section: Superfield Supercurrentmentioning

confidence: 99%

Superfield formulation of central charge anomalies in two-dimensional supersymmetric theories with solitons

Shizuya

2004

Phys. Rev. D

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“…The third term can be absorbed into the mass term of Eq. ( 27), leaving only the 1st term as the anomaly [23]. Therefore…”

Section: Fujikawa Calculationmentioning

confidence: 99%

Path-integral approach to scale anomaly at finite temperature

Lin

Ordóñez

2015

Phys. Rev. D

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We derive the relativistic thermodynamic scale equation using imaginary-time path integrals, with complex scalar field theory taken as a concrete example. We use Fujikawa's method to derive the scaling anomaly for this system using a matrix regulator. We make a general scaling argument to show how for anomalous systems, the β function of the vacuum theory can be derived from measurement of macroscopic thermodynamic parameters.

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“…Therefore 2E − DP is also a measure of the anomaly for classically scale-invariant systems. [14,15] that the trace of the improved stress-energy tensor in relativistic λφ 4 has the property θ 00 − i θ ii = m 2 φ 2 , where the mass term represents a dilational symmetry-breaking term and the improved stress-energy tensor θ µν is related to the canonical one T µν by [16]. Identifying θ 00 as E and i θ ii = DP H , where P H is the hydrodynamic pressure, one derives the thermal analog.…”

Section: With This Convention 2ementioning

confidence: 99%

Dilational symmetry-breaking in thermodynamics

Lin¹,

Ordóñez²

2017

J. Stat. Mech.

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Using thermodynamic relations and dimensional analysis we derive a general formula for the thermodynamical trace 2E − DP for nonrelativistic systems and E − DP for relativistic systems, where D is the number of spatial dimensions, in terms of the microscopic scales of the system within the grand canonical ensemble. We demonstrate the formula for several cases, including anomalous systems which develop scales through dimensional transmutation. Using this relation, we make explicit the connection between dimensional analysis and the virial theorem. This paper is focused mainly on the non-relativistic aspects of this relation.

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Path-integral formulation of conformal anomalies

Cited by 12 publications

References 10 publications

Superfield formulation of central charge anomalies in two-dimensional supersymmetric theories with solitons

Superfield formulation of central charge anomalies in two-dimensional supersymmetric theories with solitons

Path-integral approach to scale anomaly at finite temperature

Dilational symmetry-breaking in thermodynamics

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