Higher dimensional higher derivative ϕ4 theory

Higher dimensional higher derivative ϕ4 theory We construct several towers of scalar quantum field theories with an O(N) symmetry which have higher derivative kinetic terms. The Lagrangians in each tower are connected by lying in the same universality class at the d-dimensional Wilson-Fisher fixed point. Moreover the universal theory is studied using the large N expansion and we determine d-dimensional critical exponents to O(1/N2). We show that these new universality classes emerge naturally as solutions to the linear relation of the dimensions of the fields deduced from the underlying force-matter interaction of the universal critical theory. To substantiate the equivalence of the Lagrangians in each tower we renormalize each to several loop orders and show that the renormalization group functions are consistent with the large N critical exponents. While we focus on the first two new towers of theories and renormalize the respective Lagrangians to 16 and 18 dimensions there are an infinite number of such towers. We also briefly discuss the conformal windows and the extension of the ideas to theories with spin-12 and spin-1 fields as well as the idea of lower dimension completeness. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Higher dimensional higher derivative ϕ4 theory

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Higher dimensional higher derivative ϕ4 theory

Abstract

We construct several towers of scalar quantum field theories with an O(N) symmetry which have higher derivative kinetic terms. The Lagrangians in each tower are connected by lying in the same universality class at the d-dimensional Wilson-Fisher fixed point. Moreover the universal theory is studied using the large N expansion and we determine d-dimensional critical exponents to O(1/N2). We show that these new universality classes emerge naturally as solutions to the linear relation of the dimensions of the fields deduced from the underlying force-matter interaction of the universal critical theory. To substantiate the equivalence of the Lagrangians in each tower we renormalize each to several loop orders and show that the renormalization group functions are consistent with the large N critical exponents. While we focus on the first two new towers of theories and renormalize the respective Lagrangians to 16 and 18 dimensions there are an infinite number of such towers. We also briefly discuss the conformal windows and the extension of the ideas to theories with spin-12 and spin-1 fields as well as the idea of lower dimension completeness.
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Publisher
The American Physical Society
Copyright
Copyright © © 2017 American Physical Society
ISSN
1550-7998
eISSN
1550-2368
D.O.I.
10.1103/PhysRevD.96.025022
Publisher site
See Article on Publisher Site

Abstract

We construct several towers of scalar quantum field theories with an O(N) symmetry which have higher derivative kinetic terms. The Lagrangians in each tower are connected by lying in the same universality class at the d-dimensional Wilson-Fisher fixed point. Moreover the universal theory is studied using the large N expansion and we determine d-dimensional critical exponents to O(1/N2). We show that these new universality classes emerge naturally as solutions to the linear relation of the dimensions of the fields deduced from the underlying force-matter interaction of the universal critical theory. To substantiate the equivalence of the Lagrangians in each tower we renormalize each to several loop orders and show that the renormalization group functions are consistent with the large N critical exponents. While we focus on the first two new towers of theories and renormalize the respective Lagrangians to 16 and 18 dimensions there are an infinite number of such towers. We also briefly discuss the conformal windows and the extension of the ideas to theories with spin-12 and spin-1 fields as well as the idea of lower dimension completeness.

Journal

Physical Review DAmerican Physical Society (APS)

Published: Jul 15, 2017

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