The authors automate matching of generic 3D dimension-five and -six operators for arbitrary models, implemented in an extension of DRalgo with public code and examples for scalar-Yukawa, hot QCD, and the full Standard Model.
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Heat kernel expansion: user's manual
Mixed citation behavior. Most common role is background (62%).
32
Pith papers citing it
Background
62% of classified citations
abstract
The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients scattered in mathematical and physical literature. We present explicit expressions for these coefficients on manifolds with and without boundaries, subject to local and non-local boundary conditions, in the presence of various types of singularities (e.g., domain walls). In each case the heat kernel coefficients are given in terms of several geometric invariants. These invariants are derived for scalar and spinor theories with various interactions, Yang-Mills fields, gravity, and open bosonic strings. We discuss the relations between the heat kernel coefficients and quantum anomalies, corresponding anomalous actions, and covariant perturbation expansions of the effective action (both "low-" and "high-energy" ones).
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representative citing papers
A spectral cutoff RG flow on S^3 realizes the Wilson-Fisher universality class with one relevant direction and critical exponents close to flat-space values.
The scheme-independent 3-sphere free energy decreases at O(g^2) under relevant deformations of a 3D CFT but is not monotone along the full RG flow of the free massive scalar on S^3.
A conformal gauge theory for vector-spinors is constructed that is Weyl invariant when massless, propagates a massive spin-3/2 mode together with a negative-norm spin-1/2 state of double the mass, and satisfies the Hofman-Maldacena bound on the anomaly coefficient.
A new Functional Dimensional Regularization scheme computes Ising critical exponents directly in d=3 with apparently better convergence than standard functional RG approximations.
The index of non-Hermitian Dirac operators that anticommute with a chirality operator is topologically protected when the operators are diagonalizable and elliptic.
A worldline image method is developed for the Yang-Mills effective action with boundaries, checked via the first three Seeley-DeWitt coefficients and applied to chromoelectric gluon production.
No half-dimensional gravitino boundary condition—local or APS-type—closes the preserved chiral supersymmetry with Witten's conformal bosonic data; the trace-free extrinsic curvature is both the free response and the supersymmetry obstruction.
Constructs anomaly-preserving double-current deformations of 2D QFTs via dynamical gauge and Stueckelberg fields, reducing to a holonomy integral kernel that yields a Gaussian transform for the compact boson partition function.
Macroscopic computation of charge-ratio logarithmic corrections to black hole entropy agrees with microscopic results in N=4 and N=8 string theories after including string-scale cutoff, dilaton-dependent measure, Kalb-Ramond variable, and microcanonical ensemble.
Real acceleration strengthens deconfining properties of gluonic matter per the one-loop Polyakov-loop potential minimized in the optical metric, while imaginary acceleration yields a confined phase.
The paper proposes that condensate competition in the 2d Gross-Neveu model generates an emergent AdS₃ bulk, a higher-spin tower, D1-branes, and linearized Einstein gravity with G₃ = ℓ_AdS/4πN².
Develops a Lagrangian path integral formulation for non-projectable Hořava gravity and computes one-loop divergences in (2+1) dimensions, verifying cancellation of linear-in-frequency terms to extract beta functions for Newton constant and λ.
Semiclassical one-loop analysis of solvable near-critical collapse solutions shows quantum corrections selecting a Boulware-like state and producing a growing mode that yields a finite mass gap and a transition to Type I behavior, enforcing weak cosmic censorship.
The one-loop graviton path integral on S² × S^{d-1} factorizes into a bulk thermal graviton gas partition function in Nariai geometry and an edge contribution from shift-symmetric fields on S^{d-1}.
Inner horizon saddles supply the semiclassical correction -exp(A_inner/4G) to near-extremal black-hole entropy and motivate a spectral KSW criterion for well-defined one-loop effects around complex gravitational saddles.
Deformed two-point correlators in mixed TbarT/root-TbarT CFTs admit an explicit kernel representation as weighted averages of undeformed CFT correlators over conformal dimensions, with the two-point function obtained to all orders in TbarT and leading order in root-TbarT.
A heat kernel plus background field method computes gauge-invariant beta functions and anomalous dimensions without diagrams by treating open and closed derivatives consistently.
Proper-time flow yields positive gravitational corrections to gauge beta functions and negative leading corrections to Yukawa beta functions at the Einstein-Hilbert fixed point, with quantified scheme dependence and limited room for interactive matter fixed points.
In torsionless helicoidal spacetime, mode-level linear chirality cancels in the nonchiral Casimir sum, leaving a finite quadratic helicoidal vacuum susceptibility and radial force correction.
String-scale UV cut-off in the gravitational path integral removes string-coupling dependence from the BPS black hole index in extended supergravity, matching supersymmetry expectations for zero-Euler-number cases.
The replica-energy filter (1 − d^{-1} L ∂_L) on log Z isolates universal subextensive data in thermal QFT: central charges, sphere free energies, topological degeneracies, fracton degeneracies, and the Euler anomaly.
Computes dimension-six operators in finite-temperature massive scalar QED via heat kernel methods and evaluates their combined effect with the Polyakov loop on first-order phase transition thermodynamics.
Worldsheet effects from wedge singularities plus D0-brane emergence reproduce the tree-level tachyon mass in type 0A strings within a specific scaling limit.
citing papers explorer
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Matching higher-dimensional operators at finite temperature for general models
The authors automate matching of generic 3D dimension-five and -six operators for arbitrary models, implemented in an extension of DRalgo with public code and examples for scalar-Yukawa, hot QCD, and the full Standard Model.
-
Coarse graining from within: Wilson-Fisher universality on $S^3$
A spectral cutoff RG flow on S^3 realizes the Wilson-Fisher universality class with one relevant direction and critical exponents close to flat-space values.
-
The scheme independent 3-sphere free energy is not a monotone F-function
The scheme-independent 3-sphere free energy decreases at O(g^2) under relevant deformations of a 3D CFT but is not monotone along the full RG flow of the free massive scalar on S^3.
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Conformal gauge theory of vector-spinors and spin-3/2 particles
A conformal gauge theory for vector-spinors is constructed that is Weyl invariant when massless, propagates a massive spin-3/2 mode together with a negative-norm spin-1/2 state of double the mass, and satisfies the Hofman-Maldacena bound on the anomaly coefficient.
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Rethinking Dimensional Regularization in Critical Phenomena
A new Functional Dimensional Regularization scheme computes Ising critical exponents directly in d=3 with apparently better convergence than standard functional RG approximations.
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Atiyah--Singer Index Theorem for Non-Hermitian Dirac Operators
The index of non-Hermitian Dirac operators that anticommute with a chirality operator is topologically protected when the operators are diagonalizable and elliptic.
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Worldline Images for Yang-Mills Theory within Boundaries
A worldline image method is developed for the Yang-Mills effective action with boundaries, checked via the first three Seeley-DeWitt coefficients and applied to chromoelectric gluon production.
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A Linearized Obstruction to the Supersymmetric Extension of Conformal Boundary Conditions in Euclidean Gravity
No half-dimensional gravitino boundary condition—local or APS-type—closes the preserved chiral supersymmetry with Witten's conformal bosonic data; the trace-free extrinsic curvature is both the free response and the supersymmetry obstruction.
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Double-Current Deformations of Two-Dimensional QFTs with Anomalies
Constructs anomaly-preserving double-current deformations of 2D QFTs via dynamical gauge and Stueckelberg fields, reducing to a holonomy integral kernel that yields a Gaussian transform for the compact boson partition function.
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Logarithm of charge ratio in black hole entropy
Macroscopic computation of charge-ratio logarithmic corrections to black hole entropy agrees with microscopic results in N=4 and N=8 string theories after including string-scale cutoff, dilaton-dependent measure, Kalb-Ramond variable, and microcanonical ensemble.
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Polyakov-loop potential of accelerated gluonic matter and subtlety in thermodynamics
Real acceleration strengthens deconfining properties of gluonic matter per the one-loop Polyakov-loop potential minimized in the optical metric, while imaginary acceleration yields a confined phase.
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Higher-spin composites and emergent AdS$_3$ geometry in the $(1+1)$-dimensional Gross-Neveu model
The paper proposes that condensate competition in the 2d Gross-Neveu model generates an emergent AdS₃ bulk, a higher-spin tower, D1-branes, and linearized Einstein gravity with G₃ = ℓ_AdS/4πN².
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Quantizing non-projectable Ho\v{r}ava gravity with Lagrangian path integral
Develops a Lagrangian path integral formulation for non-projectable Hořava gravity and computes one-loop divergences in (2+1) dimensions, verifying cancellation of linear-in-frequency terms to extract beta functions for Newton constant and λ.
-
Unveiling horizons in quantum critical collapse
Semiclassical one-loop analysis of solvable near-critical collapse solutions shows quantum corrections selecting a Boulware-like state and producing a growing mode that yields a finite mass gap and a transition to Type I behavior, enforcing weak cosmic censorship.
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Gravitons on Nariai Edges
The one-loop graviton path integral on S² × S^{d-1} factorizes into a bulk thermal graviton gas partition function in Nariai geometry and an edge contribution from shift-symmetric fields on S^{d-1}.
-
Inner Horizon Saddles and a Spectral KSW Criterion
Inner horizon saddles supply the semiclassical correction -exp(A_inner/4G) to near-extremal black-hole entropy and motivate a spectral KSW criterion for well-defined one-loop effects around complex gravitational saddles.
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Correlators in $T\bar{T}$ and Root-$T\bar{T}$ Deformed CFTs
Deformed two-point correlators in mixed TbarT/root-TbarT CFTs admit an explicit kernel representation as weighted averages of undeformed CFT correlators over conformal dimensions, with the two-point function obtained to all orders in TbarT and leading order in root-TbarT.
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Background Fields Meet the Heat Kernel: Gauge Invariance and RGEs without diagrams
A heat kernel plus background field method computes gauge-invariant beta functions and anomalous dimensions without diagrams by treating open and closed derivatives consistently.
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Quantum gravity contributions to the gauge and Yukawa couplings in proper time flow
Proper-time flow yields positive gravitational corrections to gauge beta functions and negative leading corrections to Yukawa beta functions at the Einstein-Hilbert fixed point, with quantified scheme dependence and limited room for interactive matter fixed points.
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Geometry-induced Casimir response in a helicoidal spacetime
In torsionless helicoidal spacetime, mode-level linear chirality cancels in the nonchiral Casimir sum, leaving a finite quadratic helicoidal vacuum susceptibility and radial force correction.
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Extended Supergravity Needs String Scale Cut-off
String-scale UV cut-off in the gravitational path integral removes string-coupling dependence from the BPS black hole index in extended supergravity, matching supersymmetry expectations for zero-Euler-number cases.
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Nonadditivity in Quantum Field Theory: Replica Energies, Scaling Filters, and the Renormalization Group
The replica-energy filter (1 − d^{-1} L ∂_L) on log Z isolates universal subextensive data in thermal QFT: central charges, sphere free energies, topological degeneracies, fracton degeneracies, and the Euler anomaly.
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Higher-dimensional operators and Polyakov loop in hot Scalar QED from the heat kernel
Computes dimension-six operators in finite-temperature massive scalar QED via heat kernel methods and evaluates their combined effect with the Polyakov loop on first-order phase transition thermodynamics.
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String dualities and wedge singularities
Worldsheet effects from wedge singularities plus D0-brane emergence reproduce the tree-level tachyon mass in type 0A strings within a specific scaling limit.
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Complex Geodesics in the Nariai Geometry
Obtains the two-point correlator in Nariai geometry as a sum over complex geodesics via heat kernel approximation on sphere products followed by analytic continuation, extending de Sitter results.
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Proper-time functional renormalization in $O(N)$ scalar models coupled to gravity
Proper-time FRG applied to gravity-coupled O(N) scalars largely reproduces scaling solutions and critical properties found with the effective average action, with some quantitative differences at finite and large N depending on improved schemes.
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Instabilities in scale-separated Casimir vacua
Casimir-stabilized AdS vacua with parametric scale separation in supergravity exhibit perturbative and non-perturbative instabilities under deformations.
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Theoretical and Observational Bounds on Dynamical Chern-Simons Gravity as an Effective Field Theory
Causality from Shapiro delay and UV species/perturbativity bounds force the dynamical Chern-Simons coupling to be tiny for macroscopic gravitational systems.
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On Padmanabhan's duality invariance and the quantum of length
O(ℓ²) corrections to Padmanabhan's duality-invariant propagator are realized by a free massive scalar field in Euclidean R^{D+2}.
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One-loop divergences for KK theories on $\mathrm{AdS}\times S$ spaces; a reanalysis of $\mathrm{AdS}_4 \times S^7\,\big/$ ABJM precision holography
New framework for one-loop log divergences on AdS x S spaces recovers the 1/4 log N ABJM correction from 11d SUGRA in 4d language.
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Spectral Noncommutative Geometry, Standard Model and all that
Review of spectral noncommutative geometry applied to the Standard Model, including bosonic and fermionic actions, Euclidean vs Lorentz issues, and going beyond the SM.
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Asymptotically safe quantum gravity and its phenomenology -- a review
Review surveying progress toward realistic asymptotically safe quantum gravity with quantum scale symmetry and observational implications.