Anomalous Dimensions of Monopole Operators at the Transitions between Dirac and Topological Spin Liquids

Dupuis, Éric; Boyack, Rufus; Witczak-Krempa, William

doi:10.1103/physrevx.12.031012

Cited by 12 publications

(10 citation statements)

References 92 publications

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“…Besides, the leading SO (5) traceless symmetric (T ) scalar is constructed by the charge 1 monopoles and fermion bilinears in N f = 2 QED 3 -GNY model or quadrilinear of the matter fields in NCCP 1 model. Above recipes of SO (5) representations are helpful to test the emergent SO(5) symmetry and dualities using lattice simulations [31,32,[45][46][47] or perturbative approaches [17,[48][49][50]. The results provide promising evidence for the emergent SO(5) symmetry and dualities.…”

Section: Bootstrap Bounds On So(5) Dqcpmentioning

confidence: 94%

Bootstrapping conformal QED3 and deconfined quantum critical point

2022

J. High Energ. Phys.

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We bootstrap the deconfined quantum critical point (DQCP) and 3D Quantum Electrodynamics (QED3) coupled to Nf flavors of two-component Dirac fermions. We show the lattice and perturbative results on the SO(5) symmetric DQCP are excluded by the bootstrap bounds with an assumption that the lowest singlet scalar is irrelevant. Remarkably, we discover a new family of kinks in the 3D SO(N) vector bootstrap bounds with N ⩾ 6. We demonstrate coincidences between SU(Nf) adjoint and $$ \textrm{SO}\left({N}_f^2-1\right) $$ SO N f 2 − 1 vector bootstrap bounds due to a novel algebraic relation between the crossing equations. By introducing gap assumptions breaking the $$ \textrm{SO}\left({N}_f^2-1\right) $$ SO N f 2 − 1 symmetry, the SU(Nf) adjoint bootstrap bounds with large Nf converge to the 1/Nf perturbative results of QED3. Our results provide strong evidence that the SO(5) DQCP is not continuous and the critical flavor number of QED3 is slightly above 2: $$ {N}_f^{\ast}\in \left(2,4\right) $$ N f ∗ ∈ 2 4 . Bootstrap results near $$ {N}_f^{\ast } $$ N f ∗ are well consistent with the merger and annihilation mechanism for the loss of conformality in QED3.

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Section: Bootstrap Bounds On So(5) Dqcpmentioning

confidence: 94%

Bootstrapping conformal QED3 and deconfined quantum critical point

2022

J. High Energ. Phys.

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“…[58] As discussed in [7], to properly define QED3 in this case one must add various gravitational Chern-Simons terms, but these do not contribute the local CFT data we are interested in [59] Some evidence from monopole scaling dimensions was found in [34] for the duality between Gross-Neveu QED3 with two fermions and scalar QED3 with two scalars, but it is unclear if the latter theory is in fact a CFT [49][50][51], which is a prerequisite for IR duality.…”

Section: (B7)mentioning

confidence: 99%

“…In the normalization (2), the charge q is restricted by Dirac quantization to take the values q ∈ Z/2. As in [20,21,24,[26][27][28][29][30][31][32][33][34], we will compute the scaling dimension of the lowest dimension monopole operators using the state-operator correspondence, which identifies the scaling dimensions of monopole operators of charge q with the energies of states in the Hilbert space on S 2 × R with 4πq magnetic flux through the sphere [20]. The ground state energy on S 2 × R can then be computed in the large N and k limit using a saddle point expansion.…”

mentioning

confidence: 99%

“…For other operators in scalar QED3 that are constructed from matter fields, such as the lowest dimension singlet computed for k = 0 in [41], the large N expansion seems much less accurate when compared against lattice estimates such as [8]. Perhaps the large charge expansion [39,40] could also explain this, as this expansion was shown to work well for the scaling dimension of monopole operators [34,35]. For instance, it could be that the first couple orders at large q only receive contributions from the first couple orders in 1/N .…”

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confidence: 99%

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Evidence for 3d bosonization from monopole operators

Chester¹,

DuPuis²,

Witczak-Krempa³

2022

Preprint

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We give evidence for 3d bosonization in Conformal Field Theories (CFTs) by computing monopole operator scaling dimensions in 2+1 dimensional quantum electrodynamics (QED3) with Chern-Simons level k and N complex bosons in a large N, k expansion. We first consider the k = 0 case, where we show that scaling dimensions previously computed to subleading order in 1/N can be extrapolated to N = 1 and matched to O(2) Wilson-Fisher CFT scaling dimensions with around 5% error, which is evidence for particle-vortex duality. We then generalize the subleading calculation to large N, k and fixed k/N , extrapolate to N = k = 1, and consider monopole operators that are conjectured to be dual to non-degenerate scalar operators in a theory of a single Dirac fermion. We find matches typically with 1% error or less, which is strong evidence of this so-called 'seed' duality that implies a web of 3d bosonization dualities among CFTs.

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“…A specific generalization of the bound was also proposed for the non-Abelian global symmetry case. The conjecture was tested in a number of CFTs in [7][8][9][10], and so far is satisfied. It was also studied further in [11,12].…”

Section: Introductionmentioning

confidence: 99%

Convexity of charged operators in CFTs with multiple Abelian symmetries

Palti

Sharon

2022

J. High Energ. Phys.

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Motivated by the Weak Gravity Conjecture in the context of holography in AdS, it has been proposed that operators charged under global symmetries in CFTs, in three dimensions or higher, should satisfy certain convexity properties on their spectrum. A key element of this proposal is the charge at which convexity must appear, which was proposed to never be parametrically large. In this paper, we develop this constraint in the context of multiple Abelian global symmetries. We propose the statement that the convex directions in the multi-dimensional charge space should generate a sub-lattice of the total lattice of charged operators, such that the index of this sub-lattice cannot be made parametrically large. In the special case of two-dimensional CFTs, the index can be made parametrically large, which we prove by an explicit example. However, we also prove that in two dimensions there always exist convex directions generating a sub-lattice with an index bounded by the current levels of the global symmetry. Therefore, in two dimensions, the conjecture should be slightly modified to account for the current levels, and then it can be proven. In more than two dimensions, we show that the index of the sub-lattice generated by marginally convex charge vectors associated to BPS operators only, can be made parametrically large. However, we do not find evidence for parametric delay in convexity once all operators are considered.

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Anomalous Dimensions of Monopole Operators at the Transitions between Dirac and Topological Spin Liquids

Cited by 12 publications

References 92 publications

Bootstrapping conformal QED3 and deconfined quantum critical point

Bootstrapping conformal QED3 and deconfined quantum critical point

Evidence for 3d bosonization from monopole operators

Convexity of charged operators in CFTs with multiple Abelian symmetries

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