TY - JOUR

T1 - Boundaries and interfaces with localized cubic interactions in the O(N) model

AU - Harribey, Sabine

AU - Klebanov, Igor R.

AU - Sun, Zimo

N1 - Publisher Copyright:
© 2023, The Author(s).

PY - 2023/10

Y1 - 2023/10

N2 - We explore a new approach to boundaries and interfaces in the O(N) model where we add certain localized cubic interactions. These operators are nearly marginal when the bulk dimension is 4 − ϵ, and they explicitly break the O(N) symmetry of the bulk theory down to O(N − 1). We show that the one-loop beta functions of the cubic couplings are affected by the quartic bulk interactions. For the interfaces, we find real fixed points up to the critical value N crit ≈ 7, while for N > 4 there are IR stable fixed points with purely imaginary values of the cubic couplings. For the boundaries, there are real fixed points for all N, but we don’t find any purely imaginary fixed points. We also consider the theories of M pairs of symplectic fermions and one real scalar, which have quartic OSp(1|2M) invariant interactions in the bulk. We then add the Sp(2M) invariant localized cubic interactions. The beta functions for these theories are related to those in the O(N) model via the replacement of N by 1 − 2M. In the special case M = 1, there are boundary or interface fixed points that preserve the OSp(1|2) symmetry, as well as other fixed points that break it.

AB - We explore a new approach to boundaries and interfaces in the O(N) model where we add certain localized cubic interactions. These operators are nearly marginal when the bulk dimension is 4 − ϵ, and they explicitly break the O(N) symmetry of the bulk theory down to O(N − 1). We show that the one-loop beta functions of the cubic couplings are affected by the quartic bulk interactions. For the interfaces, we find real fixed points up to the critical value N crit ≈ 7, while for N > 4 there are IR stable fixed points with purely imaginary values of the cubic couplings. For the boundaries, there are real fixed points for all N, but we don’t find any purely imaginary fixed points. We also consider the theories of M pairs of symplectic fermions and one real scalar, which have quartic OSp(1|2M) invariant interactions in the bulk. We then add the Sp(2M) invariant localized cubic interactions. The beta functions for these theories are related to those in the O(N) model via the replacement of N by 1 − 2M. In the special case M = 1, there are boundary or interface fixed points that preserve the OSp(1|2) symmetry, as well as other fixed points that break it.

KW - 1/N Expansion

KW - Boundary Quantum Field Theory

KW - Renormalization Group

KW - Scale and Conformal Symmetries

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U2 - 10.1007/JHEP10(2023)017

DO - 10.1007/JHEP10(2023)017

M3 - Article

AN - SCOPUS:85173784956

SN - 1126-6708

VL - 2023

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 10

M1 - 17

ER -