# Reply to “Comment on ‘Topological invariants, instantons, and the chiral anomaly on spaces with torsion’ ”

@article{Chanda1997ReplyT, title={Reply to “Comment on ‘Topological invariants, instantons, and the chiral anomaly on spaces with torsion’ ”}, author={Osvaldo Chand́ıa and Jorge Zanelli}, journal={Physical Review D}, year={1997}, volume={63} }

We respond to the comment by Kreimer et. al. about the torsional contribution to the chiral anomaly in curved spacetimes. We discuss their claims and refute its main conclusion.

## 141 Citations

### Parity violation in Poincaré gauge gravity

- Physics
- 2020

We analyze the parity violation issue in the Poincare gauge theory of gravity for the two classes of models which are built as natural extensions of the Einstein–Cartan theory. The conservation law...

### Torsional topological invariants

- MathematicsPhysical Review D
- 2018

Making use of the SO(3,1) Lorentz algebra, we derive in this paper two series of Gauss-Bonnet type identities involving torsion, one being of the Pontryagin type and the other of the Euler type. Two…

### Comments on MacDowell–Mansouri gravity and torsion

- Physics
- 2017

Starting with the MacDowell–Mansouri formulation of gravity with a SO(4, 1) gauge group, we introduce new parameters into the action to include the nondynamical Holst term, and the topological…

### Symmetries and observables in topological gravity

- Physics
- 2004

After a brief review of topological gravity, we present a superspace approach to this theory. This formulation allows us to recover in a natural manner various known results and to gain some insight…

### GRAVITATIONAL CONSTANT AND TORSION

- Physics
- 2002

Riemann–Cartan space–time U4 is considered here. It has been shown that when we link topological Nieh–Yan density with the gravitational constant, we then obtain Einstein–Hilbert Lagrangian as a…

### On torsional observables in topological 4D gravity

- Mathematics
- 2007

We construct, in topological 4D gravity with torsion, a set of observables involving the topological invariant given by integrating the Nieh–Yan (NY) 4-form. The method relies as usual on the…

### Chiral Anomaly in Contorted Spacetimes

- Physics
- 1999

The Dirac equation in Riemann-Cartan spacetimeswith torsion is reconsidered. As is well-known, only theaxial covector torsion A, a oneform, couples to massiveDirac fields. Using diagrammatic…

### The Holst Action by the Spectral Action Principle

- Mathematics
- 2011

We investigate the Holst action for closed Riemannian 4-manifolds with orthogonal connections. For connections whose torsion has zero Cartan type component we show that the Holst action can be…

### The Chiral Heat Effect

- Physics
- 2012

(Received January 3, 2012; Revised May 1, 2012)We consider the thermal response of a (3+1)-dimensional theory with a chiral anomalyonacurved space motivatedbythechiralmagneticeﬀect. Weﬁnd anew…

## References

SHOWING 1-10 OF 26 REFERENCES

### On the chiral anomaly in non-Riemannian spacetimes

- Mathematics
- 1997

Thetranslation Chern-Simons type three-formcoframe∧torsion on a Riemann-Cartan spacetime is related (by differentiation) to the Nieh-Yan fourform. Following Chandia and Zanelli, two spaces with…

### Massive torsion modes from Adler-Bell-Jackiw and scaling anomalies

- Physics
- 1999

Regularization of quantum field theories introduces a mass scale which breaks axial rotational and scaling invariances. We demonstrate from first principles that axial torsion and torsion trace modes…

### Selected topics in gauge theories

- Physics
- 1986

Developments in gauge field theory in the past fourteen years are discussed. The canonical description of electroweak and strong interactions is described including the role played by QCD and QFD.…

### Torsional topological invariants (and their relevance for real life)

- Mathematics
- 1997

The existence of topological invariants analogous to Chern/Pontryagin classes for a standard SO(D) or SU(N) connection, but constructed out of the torsion tensor, is discussed. These invariants…

### Class

- Quantum Grav. 8, 1545
- 1991

### Phys

- 23, 373
- 1982

### Class

- Quantum Grav. 13, 2423
- 1996

### Prog

- Theo. Phys. 74, 866
- 1985

### Phys

- Lett. B 108, 308 (1982);Nucl. Phys. B 212, 237 (1983); Jour. Phys A 16, 3795
- 1983