Rotation-driven current under a deformed density of states
The chiral vortical effect is the response in which rotation produces a vector or axial current along the vorticity direction in matter made of chiral fermions. In equilibrium, the leading coefficients of this response are tied to gauge and mixed gauge-gravitational anomalies rather than to ordinary dissipative transport. This paper asks whether an isotropic minimal-length deformation of the momentum-space density of states can disturb that anomaly-controlled leading structure.
The deformation is treated semiclassically through a generalized uncertainty principle, in which the canonical position-momentum algebra receives momentum-dependent corrections. At the level relevant here, the minimal length changes the momentum-space density of states and therefore the weighting of equilibrium momentum integrals. The paper isolates this density-of-state sector: the current vertex, the Belinfante stress-tensor vertex, the chirality assignment, and the parity-odd tensor structure are all kept at their undeformed free-theory forms, and the deformation enters only through a scalar factor W_beta(P) multiplying the spatial momentum integral.
The vortical conductivity sigma_V is defined by the constitutive relation J^i = sigma_V omega^i, with omega the vorticity. It is extracted from the parity-odd part of the mixed current-momentum-density correlator in the static, long-wavelength Kubo limit, with the external spatial momentum taken along the rotation axis. The paper stresses that this transport coefficient is conceptually distinct from measured spin observables: global hyperon polarization establishes that a vortical environment exists, but it is not by itself a direct measurement of the chiral vortical conductivity.
The familiar mu-squared and T-squared terms keep their values
For a single right-handed Weyl fermion of unit charge, the undeformed conductivity is sigma_V^(0) = mu^2/(4 pi^2) + T^2/12. This is the standard result, and it is what the anomaly structure constrains.
Expanding the deformed integral to first order in the deformation parameter beta gives sigma_V^GUP = mu^2/(4 pi^2) + T^2/12 - beta [3 mu^4/(8 pi^2) + 3 mu^2 T^2/4 + 7 pi^2 T^4/40] + O(beta^2). The important structural point is what is absent: there is no independent O(beta mu^2) or O(beta T^2) term. Within the density-of-state sector considered, the coefficients of the standard degree-two contributions retain their undeformed right-handed Weyl values, and the leading minimal-length correction is a homogeneous degree-four polynomial in mu and T.
The paper is explicit that dimensional analysis fixes this thermodynamic degree but not the numerical coefficients, their relative sign, or their dependence on chiral charge content. Those features follow from the parity-odd Kubo correlator, not from dimensional reasoning alone.
Higher-order corrections split across anomaly and non-anomaly traces
The paper classifies the beta-dependent terms by their chiral charge content rather than by their powers of mu and T alone. This matters because a term can carry the same charge trace as an anomalous contribution while having a coefficient that the anomaly polynomial does not fix.
Among the degree-four corrections, the mixed chemical-potential thermal and purely thermal terms carry the chiral traces associated with the gauge and mixed gauge-gravitational anomaly structures. The purely quartic chemical-potential contribution instead contains an independent fifth-order chiral charge trace. The coefficients of these higher-order terms depend on the form of the density-of-state modification and are therefore not fixed by the usual four-dimensional anomaly structure.
The paper frames this as a statement about the density-of-state contribution it isolates, not as a general nonrenormalization theorem for a microscopic GUP-deformed chiral field theory. In a source-covariant formulation, additional propagator, vertex, contact, and Ward-identity contributions could arise beyond this sector.
A positive minimal-length parameter suppresses the contribution exactly
The weak-deformation expansion is not the whole story. From the exact integral representation, the Kempf-Mangano-Mann density-of-state contribution for the single right-handed unit-charge Weyl fermion satisfies d sigma_V^KMM / d beta = -(3/2 pi^2) integral dP P^3/(1 + beta P^2)^4 [n_F(P - mu) + n_F(P + mu)] < 0 for beta > 0.
Because the integrand is positive, the suppression of the density-of-state contribution is exact for positive beta within this framework, not merely an artifact of truncating the series at first order. The first-order expression in beta is the leading expansion of this exact behavior when beta times the larger of mu^2 and T^2 is much less than one; outside that domain the unexpanded integral governs the result.
This is the paper's sharpest single-species statement: for the Kempf-Mangano-Mann form, increasing the minimal-length parameter always lowers the density-of-state contribution to the vortical conductivity.
The result extends to general massless chiral multiplets
The analysis begins with a single right-handed Weyl fermion and is then extended to general massless chiral fermion systems with mutually commuting conserved charges. The extension makes explicit the roles of the gauge-anomaly trace d_ABC, the mixed gauge-gravitational trace b_A, and higher chiral charge traces.
The parity-odd Kubo analysis shows that an isotropic density-of-state deformation modifies the radial thermal moments without enlarging the vortical tensor structure. The deformation factor is a rotational scalar that depends only on the radial momentum variable, carries no Matsubara-frequency dependence, and is independent of the angular variable and the helicity labels. It therefore commutes with the helicity sums, the angular integration, and the ordered static limit, changing only the final radial weight.
The paper also notes a convention point that matters for reading the derivation: the anomaly relation is written in the covariant-current normalization, which should be distinguished from the normalization used in the thermal Kubo derivation, where the chemical potential enters through shifted fermionic Matsubara frequencies and no separate background Chern-Simons contribution is added to the mixed correlator.
A Planck-suppressed correction is negligible at chemical freeze-out
The paper assesses the size of the minimal-length contribution under standard heavy-ion chemical freeze-out conditions and finds that a Planck-suppressed correction is extremely small. The comparison uses chemical freeze-out relations to estimate the size of the density-of-state contribution in that setting.
This size statement is separate from the sign and structure results. The exact monotonic suppression for positive beta is a statement about the density-of-state contribution within the framework; the heavy-ion estimate is a statement about how large that contribution would be along standard freeze-out trajectories. Both are needed to judge whether the effect is worth pursuing observationally.
The paper also keeps separate the transport coefficient from momentum-dependent spin observables, and treats beam-energy dependence as a distinct question from the equilibrium Kubo derivation.
Where the deformation can and cannot show up
The paper's own summary is that isotropic minimal-length modifications can change higher-order contributions to chiral vortical transport while leaving the familiar leading anomaly-related response unchanged within the density-of-state sector considered. That is the priority for a reader: the leading mu^2 and T^2 coefficients are not the place to look for a minimal-length signature in this framework.
The place to look is the degree-four sector, and there the paper's comparison is between two kinds of terms. Some carry the same chiral charge combinations that appear in gauge and mixed gauge-gravitational anomalies; another carries an independent higher-order charge combination. Because their coefficients depend on the form of the density-of-state modification, they are not fixed by the four-dimensional anomaly polynomial, which is precisely why they can differ between deformation choices.
The practical threshold follows from the two results together. For the Kempf-Mangano-Mann deformation, the sign of the density-of-state contribution is fixed and monotonic in beta, so the qualitative direction does not depend on how small beta is. The magnitude, however, is governed by whether beta times the larger of mu^2 and T^2 is small, and under standard heavy-ion chemical freeze-out conditions a Planck-suppressed correction is extremely small. The paper's most decision-relevant distinction is therefore between the robust structural statement about higher-order terms and the size question, which the freeze-out estimate answers negatively for a Planck-suppressed deformation.
Sources used in this answer
Chiral vortical transport under minimal-length deformations in rotating relativistic matter
For a single right-handed Weyl fermion, an isotropic minimal-length density-of-state deformation leaves the leading chiral vortical conductivity mu^2/(4 pi^2) + T^2/12 unchanged at first order, with minimal-length effects appearing only as a degree-four polynomial in mu and T whose coefficients are not fixed by the four-dimensional anomaly structure; for the Kempf-Mangano-Mann deformation, a positive minimal-length parameter always reduces the density-of-state contribution.