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arXiv:1510.06942

Fermionic quantum operations: a computational framework I. Basic invariance properties

Gyula Lakos

Published Oct 15, 2015• 1 citation
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Abstract

The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case $n=2$, and FQ conform-operations in the case $n=3$. In this first part we study how the basic invariance properties of FQ operations ($n=2$) are reflected in their formal power series expansions.

DOI
10.48550/arxiv.1510.06942

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The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case n=2n=2n=2, and FQ conform-operations in the case n=3n=3n=3. In this first part we study how the basic invariance properties of FQ operations (n=2n=2n=2) are reflected in their formal power series expansions.
The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case n=2n=2n=2, and FQ conform-operations in the case n=3n=3n=3. In this second part we show some arithmetically constructible examples of FQ operations (n=2n=2n=2), concentrating on monoaxiality, related extensions, and (hyper)scaling.
We study twist operators in higher dimensional CFT’s. In particular, we express their conformal dimension in terms of the energy density for the CFT in a particular thermal ensemble. We construct an expansion of the conformal dimension in power series around n =1, with n being replica parameter. We show that the coefficients in this expansion are determined by higher point correlations of the energy-momentum tensor. In particular, the first and second terms, i.e. the first and second derivatives of the scaling dimension, have a simple universal form. We test these results using holography and free field theory computations, finding agreement in both cases. We also consider the ‘operator product expansion’ of spherical twist operators and finally, we examine the behaviour of correlators of twist operators with other operators in the limit n → 1.