Chern-Simons theory coupled to bifundamental scalars
TL;DR: In this article, the authors studied the three-dimensional theory of two Chern-Simons field coupled to a scalar field in the bifundamental representation of the SU(N ) −k × SU(M )−k gauge group and showed that this theory possesses a line of fixed points at any value of M/N.
Abstract: We study the three-dimensional theory of two Chern-Simons gauge fields coupled to a scalar field in the bifundamental representation of the SU(N )
k
× SU(M )−k
gauge group. At small but fixed M ≪ N , this system approaches the theory of a Chern-Simons field coupled to fundamental matter, conjectured to be dual to a parity-violating version of Vasiliev’s higher-spin gauge theory in AdS4. At finite M/N and large ’t Hooft coupling this theory (or its SUSY version) is expected to be dual to an Einstein-like gravity. We show at two loops that this theory possesses a line of fixed points at any value of M/N . We also prove that turning on a finite but small M/N gaps out the light states that Chern-Simons theory coupled to fundamental matter develops when placed on a torus. We also comment on the higher genus case.
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TL;DR: In this paper, it was shown that the symmetric product orbifold CFT is dual to the tensionless limit of string theory on AdS3 × S3 × = 4 cosets of arXiv:1305.4181.
Abstract: It is natural to believe that the free symmetric product orbifold CFT is dual to the tensionless limit of string theory on AdS3 × S3 × $$ {\mathbb{T}}^4 $$
. At this point in moduli space, string theory is expected to contain a Vasiliev higher spin theory as a subsector. We confirm this picture explicitly by showing that the large level limit of the $$ \mathcal{N} $$
=4 cosets of arXiv:1305.4181, that are dual to a higher spin theory on AdS3, indeed describe a closed subsector of the symmetric product orbifold. Furthermore, we reorganise the full partition function of the symmetric product orbifold in terms of representations of the higher spin algebra (or rather its $$ {\mathcal{W}}_{\infty } $$
extension). In particular, the unbroken stringy symmetries of the tensionless limit are captured by a large chiral algebra which we can describe explicitly in terms of an infinite sum of $$ {\mathcal{W}}_{\infty } $$
representations, thereby exhibiting a vast extension of the conventional higher spin symmetry.
240 citations
TL;DR: In this paper, it was shown that the large level limit of the N=4 cosets of arXiv:1305.4181, that are dual to a higher spin theory on AdS3, indeed describes a closed subsector of the symmetric product orbifold.
Abstract: It is natural to believe that the free symmetric product orbifold CFT is dual to the tensionless limit of string theory on AdS3 x S3 x T4. At this point in moduli space, string theory is expected to contain a Vasiliev higher spin theory as a subsector. We confirm this picture explicitly by showing that the large level limit of the N=4 cosets of arXiv:1305.4181, that are dual to a higher spin theory on AdS3, indeed describe a closed subsector of the symmetric product orbifold. Furthermore, we reorganise the full partition function of the symmetric product orbifold in terms of representations of the higher spin algebra (or rather its $W_{\infty}$ extension). In particular, the unbroken stringy symmetries of the tensionless limit are captured by a large chiral algebra which we can describe explicitly in terms of an infinite sum of $W_{\infty}$ representations, thereby exhibiting a vast extension of the conventional higher spin symmetry.
133 citations
Cites background from "Chern-Simons theory coupled to bifu..."
...This is in accord with the fact that light states do not arise in a gauge theory with adjoint fields whereas they are ubiquitous in a theory with fundamental fields on a space which allows nontrivial gauge holonomies [64, 65]....
[...]
TL;DR: In this article, it was shown that non-supersymmetric bosonization holds for all planar correlators of single-trace operators with both a scalar and a fermion.
Abstract: Three dimensional bosonization is a conjectured duality between non-super-symmetric Chern-Simons theories coupled to matter fields in the fundamental representation of the gauge group. There is a well-established supersymmetric version of this duality, which involves Chern-Simons theories with $$ \mathcal{N}=2 $$
supersymmetry coupled to fundamental chiral multiplets. Assuming that the supersymmetric duality is valid, we prove that non-supersymmetric bosonization holds for all planar correlators of single-trace operators. The main tool we employ is a double-trace flow from the supersymmetric theory to an IR fixed point, in which the scalars and fermions are effectively decoupled in the planar limit. A generalization of this technique can be used to derive the duality mapping of all renormalizable couplings, in non-supersymmetric theories with both a scalar and a fermion. Our results do not rely on an explicit computation of planar diagrams.
118 citations
Cites background from "Chern-Simons theory coupled to bifu..."
...So far, the only direct evidence supporting bosonization comes from computations done in the large N limit [1–7, 12–22] (see also [23–29] for related work)....
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TL;DR: In this paper, the scaling dimensions of the higher-spin operators of the Chern-Simons gauge theories coupled to massless fundamental scalars or fermions are computed in leading order in the 1/N expansion and exactly in the ’t Hooft coupling.
Abstract: Chern-Simons gauge theories coupled to massless fundamental scalars or fermions define interesting non-supersymmetric 3d CFTs that possess approximate higher-spin symmetries at large N In this paper, we compute the scaling dimensions of the higher-spin operators in these models, to leading order in the 1/N expansion and exactly in the ’t Hooft coupling We obtain these results in two independent ways: by using conformal symmetry and the classical equations of motion to fix the structure of the current non-conservation, and by a direct Feynman diagram calculation The full dependence on the ’t Hooft coupling can be restored by using results that follow from the weakly broken higher-spin symmetry This analysis also allows us to obtain some explicit results for the non-conserved, parity-breaking structures that appear in planar three-point functions of the higher-spin operators At large spin, we find that the anomalous dimensions grow logarithmically with the spin, in agreement with general expectations This logarithmic behavior disappears in the strong coupling limit, where the anomalous dimensions turn into those of the critical O(N ) or Gross-Neveu models, in agreement with the conjectured 3d bosonization duality
90 citations
TL;DR: In this paper, the authors conjecture that the bosonic and fermionic RG flows are dual to each other under a map of parameters under which the two partition functions agree exactly with each other all the way from the UV to the IR.
Abstract: It has previously been conjectured that the theory of free fundamental scalars minimally coupled to a Chern Simons gauge field is dual to the theory of critical fundamental fermions minimally coupled to a level rank dual Chern Simons gauge field. In this paper we study RG flows away from these two fixed points by turning on relevant operators. In the ’t Hooft large N limit we compute the thermal partition along each of these flows and find a map of parameters under which the two partition functions agree exactly with each other all the way from the UV to the IR. We conjecture that the bosonic and fermionic RG flows are dual to each other under this map of parameters. Our flows can be tuned to end at the gauged critical scalar theory and gauged free fermionic theories respectively. Assuming the validity of our conjecture, this tuned trajectory may be viewed as RG flow from the gauged theory of free bosons to the gauged theory of free fermions.
62 citations
Cites background from "Chern-Simons theory coupled to bifu..."
...We now have several exact results for correlation functions of local gauge invariant operators [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], thermal partition functions [4, 17, 18, 19, 20, 21, 22, 23] (see also [24, 25]) and S matrices [26, 27, 28] in these and related theories....
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References
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TL;DR: In this paper, it was shown that 2+1 dimensional quantum Yang-Mills theory with an action consisting purely of the Chern-Simons term is exactly soluble and gave a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.
Abstract: It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized fromS
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