Monodromy defects in free field theories

Abstract

We study co-dimension two monodromy defects in theories of conformally coupled scalars and free Dirac fermions in arbitrary d dimensions. We characterise this family of conformal defects by computing the one-point functions of the stress-tensor and conserved current for Abelian flavour symmetries as well as two-point functions of the displacement operator. In the case of d = 4, the normalisation of these correlation functions are related to defect Weyl anomaly coefficients, and thus provide crucial information about the defect conformal field theory. We provide explicit checks on the values of the defect central charges by calculating the universal part of the defect contribution to entanglement entropy, and further, we use our results to extract the universal part of the vacuum Rényi entropy. Moreover, we leverage the non-supersymmetric free field results to compute a novel defect Weyl anomaly coefficient in a d = 4 theory of free $$ \mathcal{N} $$ N = 2 hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free d = 4 Maxwell theory and show that their central charges vanish.

Localized magnetic field in the O(N) model

“…These mostly focused on spin impurities, which involve additional degrees of freedom localized on the line [19][20][21][22][23][24][25][26]. Other works focused on symmetry (twist) defects [27][28][29][30][31] (which are not genuine line defects, since they are attached to a nontrivial topological surface). Finally, we note that correlation functions with two insertions of the line defect (1.3) were recently considered in [32] for a free bulk theory and, after an earlier version of this work appeared, in [33] for the bulk interacting theory.…”

“…This provides a strong crosscheck JHEP02(2022)134 for both methods. 29 Another check for the large N computation is the following. For the trivial defect we can repeat the above computation with s 0 = 0 that corresponds to m 2 = −(4 − d)(d − 2)/4.…”

Weyl anomalies of four dimensional conformal boundaries and defects

“…Separately, in ref. [132] monodromy defects were analyzed using defect Operator Product Expansion (OPE) and free field techniques in R d . In particular, in d = 4 ref.…”

“…In particular, in d = 4 ref. [132] related the one-point function of the U(1) flavor current, J µ , as well as D i D j and T µν | Σ 2 , to the defect central charges a (2d) Σ , d (2d) 1 , and d (2d) 2 , respectively. In a similar fashion, we will use the form of the defect Weyl anomaly in eq.…”

“…If we consider a spherical monodromy defect, then ref. [132] showed that, for d even, C J (α) is related to the defect A-type anomaly coefficient by…”