The topological structure of Nieh-Yan form and the chiral anomaly in spaces with torsion

Li, Sheng

doi:10.1088/0305-4470/32/41/309

Cited by 21 publications

(17 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that the dimensionful constant ℓ is required for the action (12), which leads to controversy on the topological origin of this action (see, for example, Refs. [34,35,36,37,38,39]).…”

Section: Topological Effect With Torsionmentioning

confidence: 99%

The Chiral Heat Effect

Kimura¹,

Nishioka

2012

Progress of Theoretical Physics

View full text Add to dashboard Cite

We consider the thermal response of a (3+1)-dimensional theory with a chiral anomaly on a curved space motivated by the chiral magnetic effect. We find a new phenomenon, called the chiral heat effect, such that the thermal current is induced transverse to a gradient of the temperature even on a flat space. This effect is expected to be observed in QCD experiment as well as the chiral magnetic effect. We study a similar topological effect on the spacetime with a torsion. A holographic construction is also discussed with the D3/D7 and the Sakai-Sugimoto models.Comment: 11 pages; font error corrected; published versio

show abstract

“…Note that the dimensionful constant ℓ is required for the action (12), which leads to controversy on the topological origin of this action (see, for example, Refs. [34,35,36,37,38,39]).…”

Section: Topological Effect With Torsionmentioning

confidence: 99%

The Chiral Heat Effect

Kimura¹,

Nishioka

2012

Progress of Theoretical Physics

View full text Add to dashboard Cite

show abstract

“…where   C is the torsion tensor defined in (13). Following the same procedure as in deriving the identities (20) and (21), we can derive a similar identity for…”

Section: Gauss-bonnet Identitiesmentioning

confidence: 93%

“…But, the derivation presented here has the advantage of making the meaning of the topological invariant more transparent. The geometric properties of the invariant have been studied by Chandia and Zanelli [12] and others [13]. It is well known that the Pontryagin or Chern-Weil class for the Lorentz group,…”

Section: Torsional Topological Invariantmentioning

confidence: 99%

A Torsional Topological Invariant

Nieh

2007

Int. J. Mod. Phys. A

View full text Add to dashboard Cite

Curvature and torsion are the two tensors characterizing a general Riemannian space-time. In Einstein's General Theory of Gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the curvature tensor plays the central role. For such a purely metric geometry, two well-known topological invariants, namely the Euler class and the Pontryagin class, are useful in characterizing the topological properties of the space-time. From a gauge theory point of view, and especially in the presence of spin, torsion naturally comes into play, and the underlying spacetime is no longer purely metric. We describe a torsional topological invariant, discovered in 1982, that has now found increasing usefulness in recent developments.

show abstract

“…This suggests that (3) can be relevant in theories of gravity such as Einstein-Cartan or Teleparallel Equivalent General Relativity (TEGR). Topological invariants involving the torsion tensor were first constructed in [17] and further studied in [18][19][20]. They have also been used in the context of a gravitational Peccei-Quinn mechanism [21], in studies of axions in torsional gravity [22] and in the context of AdS 4 /CFT 3 holography [23].…”

Section: Introductionmentioning

confidence: 99%

Torsion-induced gravitational $$\theta $$ term and gravitoelectromagnetism

2020

View full text Add to dashboard Cite

Motivated by the analogy between a weak field expansion of general relativity and Maxwell’s laws of electrodynamics, we explore physical consequences of a parity violating $$\theta $$ θ term in gravitoelectromagnetism. This is distinct from the common gravitational $$\theta $$ θ term formed as a square of the Riemann tensor. Instead it appears as a product of the gravitoelectric and gravitomagnetic fields in the Lagrangian, similar to the Maxwellian $$\theta $$ θ term. We show that this sector can arise from a quadratic torsion term in nonlinear gravity. In analogy to the physics of topological insulators, the torsion-induced $$\theta $$ θ parameter can lead to excess mass density at the interface of regions where $$\theta $$ θ varies and consequently it generates a correction to Newton’s law of gravity. We discuss also an analogue of the Witten effect for gravitational dyons.

show abstract

The topological structure of Nieh-Yan form and the chiral anomaly in spaces with torsion

Cited by 21 publications

References 22 publications

The Chiral Heat Effect

The Chiral Heat Effect

A Torsional Topological Invariant

Torsion-induced gravitational $$\theta $$ term and gravitoelectromagnetism

Contact Info

Product

Resources

About