Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models

170

We build the framework for performing loop computations in the defect version of N = 4 super Yang-Mills theory which is dual to the probe D5-D3 brane system with background gauge-field flux. In this dCFT, a codimension-one defect separates two regions of space-time with different ranks of the gauge group and three of the scalar fields acquire non-vanishing and space-time-dependent vacuum expectation values. The latter leads to a highly non-trivial mass mixing problem between different colour and flavour components, which we solve using fuzzy-sphere coordinates. Furthermore, the resulting space-time dependence of the theory's Minkowski space propagators is handled by reformulating these as propagators in an effective AdS 4 . Subsequently, we initiate the computation of quantum corrections. The one-loop correction to the one-point function of any local gauge-invariant scalar operator is shown to receive contributions from only two Feynman diagrams. We regulate these diagrams using dimensional reduction, finding that one of the two diagrams vanishes, and discuss the procedure for calculating the one-point function of a generic operator from the SU(2) subsector. Finally, we explicitly evaluate the one-loop correction to the one-point function of the BPS vacuum state, finding perfect agreement with an earlier string-theory prediction. This constitutes a highly non-trivial test of the gauge-gravity duality in a situation where both supersymmetry and conformal symmetry are partially broken.

Section: Discussionmentioning

confidence: 99%

A quantum check of AdS/dCFT

Buhl-Mortensen¹,

Leeuw²,

Ipsen³

et al. 2017

170

“…The fuzzy spherical harmonicsŶ m of dimension k × k are given byŶ m = [Ŷ m ] n,n E n n , where the matrix elements are [41,42] [Ŷ m ] n,n = (−1) k−n √ 2 + 1…”

Section: Fuzzy Spherical Harmonics and Their Productsmentioning

confidence: 99%

“…where the curly bracket denotes a 6j symbol. The fuzzy spherical harmonics thus satisfy an algebra, the fusion algebra of fuzzy spherical harmonics [42]. Since the fusion coefficients F 3 m 3 1 m 1 2 m 2 have a Wigner 3j symbol as a factor, it is useful to be recall the selection rules for Wigner 3j symbols, which are essentially addition of angular momenta.…”

Section: Fuzzy Spherical Harmonics and Their Productsmentioning

confidence: 99%

“…Since the fusion coefficients F 3 m 3 1 m 1 2 m 2 have a Wigner 3j symbol as a factor, it is useful to be recall the selection rules for Wigner 3j symbols, which are essentially addition of angular momenta. Consider the 3j symbol in the fusion coefficients Trace formulas and α L m coefficients Since the fuzzy spherical harmonics span the space of k × k matrices, any matrix can be decomposed as an expansion inŶ m [42]. In our conventions, the generators have the expansion…”

Section: Fuzzy Spherical Harmonics and Their Productsmentioning

confidence: 99%

See 1 more Smart Citation

Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations

Leeuw¹,

Ipsen²,

Kristjansen³

et al. 2017

We calculate the leading contributions to the connected two-point functions of protected scalar operators in the defect version of N = 4 SYM theory which is dual to the D5-D3 probe-brane system with k units of background gauge field flux. This involves several types of two-point functions which are vanishing in the theory without the defect, such as two-point functions of operators of unequal conformal dimension. We furthermore exploit the operator product expansion (OPE) and the boundary operator expansion (BOE), which form the basis of the boundary conformal bootstrap equations, to extract conformal data both about the defect CFT and about N = 4 SYM theory without the defect. From the knowledge of the one-and two-point functions of the defect theory, we extract certain structure constants of N = 4 SYM theory using the (bulk) OPE and constrain certain bulkto-boundary couplings using the BOE. The extraction of the former relies on a non-trivial, polynomial k dependence of the one-point functions, which we explicitly demonstrate. In addition, it requires the knowledge of the one-point functions of SU(2) descendant operators, which we likewise explicitly determine.

“…This difference is called a noncommutative anomaly and argued to be related to UV/IR mixing [5] in the planar limit. In this theory, the Wilsonian renormalization procedure is formulated as a large-N (or a matrix) renormalization group [6,7]. The result there shows that integrating out the degrees of freedom of high energy leads to a much complicated effective action involving non-local operators.…”

Section: Introductionmentioning

confidence: 99%

Momentum-space entanglement in scalar field theory on fuzzy spheres

Kawamoto

Kuroki

2021

Self Cite

Quantum field theory defined on a noncommutative space is a useful toy model of quantum gravity and is known to have several intriguing properties, such as nonlocality and UV/IR mixing. They suggest novel types of correlation among the degrees of freedom of different energy scales. In this paper, we investigate such correlations by the use of entanglement entropy in the momentum space. We explicitly evaluate the entanglement entropy of scalar field theory on a fuzzy sphere and find that it exhibits different behaviors from that on the usual continuous sphere. We argue that these differences would originate in different characteristics; non-planar contributions and matrix regularizations. It is also found that the mutual information between the low and the high momentum modes shows different scaling behaviors when the effect of a cutoff becomes important.