My paper on non-renormalisation of anomalous conductivities in arbitrary higher derivative gravity

Arxiv preprint :
DOI: 10.1007/JHEP09(2016)046

with Sašo Grozdanov

Abstract :

Anomalous chiral conductivities in theories with global anomalies are independent of whether they are computed in a weakly coupled quantum (or thermal) field theory, hydrodynamics, or at infinite coupling from holography. While the presence of dynamical gauge fields and mixed, gauge-global anomalies can destroy this universality, in their absence, the non-renormalisation of anomalous Ward identities is expected to be obeyed at all intermediate coupling strengths. In holography, bulk theories with higher-derivative corrections incorporate coupling constant corrections to the boundary theory observables in an expansion around infinite coupling. In this work, we investigate the coupling constant dependence and universality of anomalous conductivities (and thus of the anomalous Ward identities) in general, four-dimensional systems that possess asymptotically anti-de Sitter holographic duals with a non-extremal black brane in five dimensions, and anomalous transport introduced into the boundary theory via the bulk Chern-Simons action. We show that in bulk theories with arbitrary gauge- and diffeomorphism-invariant higher-derivative actions, anomalous conductivities, which can incorporate an infinite series of (inverse) coupling constant corrections, remain universal. Owing to the existence of the membrane paradigm, the proof reduces to a construction of bulk effective theories at the horizon and the boundary. It only requires us to impose the condition of horizon regularity and correct boundary conditions on the fields. We also discuss ways to violate the universality by violating conditions for the validity of the membrane paradigm, in particular, by adding mass to the vector fields (a case with a mixed, gauge-global anomaly) and in bulk geometries with a naked singularity.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s


The companion website to Classical and Quantum Gravity

Louk Rademaker's Physics site

Theoretical Condensed Matter Physics / Quantum Matter

quantum update

อัพเดท สาระน่ารู้ เทคโนโลยีควอนตัม และ ควอนตัมคอมพิวเตอร์

Shores of the Dirac Sea

A blog about physics... mostly.

The polymath blog

Massively collaborative mathematical projects

Quantum Frontiers

A blog by the Institute for Quantum Information and Matter @ Caltech

High Energy PhDs

A discussion of particle physics and strings


"Ever tried, ever failed, no matter. Try again, fail again, fail better." - Samuel Beckett

in theory

"Marge, I agree with you - in theory. In theory, communism works. In theory." -- Homer Simpson

Gowers's Weblog

Mathematics related discussions

What's new

Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao


Fay Dowker's website

Of Particular Significance

Conversations About Science with Theoretical Physicist Matt Strassler


ปีนจากกะลา สู่โลกกว้างที่ ท้าทาย

Quendi in the UK

Love is All Around


Chinese History and Culture, Travel.

%d bloggers like this: