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3D Bosonization: Flavor-Violated, Bordered, Quivered, and Stacked

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3D Bosonization: Flavor-Violated, Bordered, Quivered, and Stacked 3d Bosonization: Flavor-Violated, Bordered, Quivered, and Stacked Kyle Aitken A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2021 Reading Committee: Laurence Yaffe, Chair Lukasz Fidkowski Andreas Karch Program Authorized to Offer Degree: Physics University of Washington Abstract 3d Bosonization: Flavor-Violated, Bordered, Quivered, and Stacked Kyle Aitken Chair of the Supervisory Committee: Professor Laurence Yaffe Physics In this work we discuss several aspects of the 3d bosonization dualities, which are a conjec- tured equivalence between Chern-Simons matter theories in 2 + 1-dimensions. We propose a new phrase diagram for the most general 3d bosonization duality when the number of matter particles is large. We discuss how the most general form the dualities can be ren- dered consistent on a manifold with boundaries. Novel quiver dualities, both bosonic and fermionic, are constructed which serve as a generalization of the well-known particle-vortex duality and which also have application to domain walls in 3 + 1-dimensional QCD. We argue the rank-one dualities can be connected to the rank-two dualities via an orbifolding procedure. Finally, we show how such 2 + 1-dimensional dualities can be related to known 3 + 1-dimensional electromagnetic duality. TABLE OF CONTENTS Page List of Figures . iii List of Tables . vii Chapter 1: Introduction to 3d Bosonization . .1 1.1 Four Systems with Dualities . .1 1.2 3d Bosonization . .6 1.3 The Master Bosonization Duality . 15 1.4 Outline . 21 Chapter 2: Flavor-Violated Dualities . 23 2.1 Review of QCD3 Symmetry-Breaking . 24 2.2 Flavor-Violated Master Duality . 27 2.3 Double-Saturated Flavor Bound . 39 2.4 Disucssion and Future Work . 40 Chapter 3: 3d Bosonization with Boundaries . 42 3.1 Notation and Preliminaries . 44 3.2 Abelian Bosonization with Boundaries . 45 3.3 Single Species non-Abelian Bosonization with Boundaries . 77 3.4 Master Duality with Boundaries . 98 3.5 Discussion . 105 Chapter 4: Building Bosonic Quivers with 3d Bosonization . 107 4.1 Non-Abelian Linear Quiver Dualities . 110 4.2 Theta Wall Dualities . 131 4.3 Adding Flavors to Quivers . 145 i 4.4 Orthogonal and Symplectic Gauge Groups . 167 4.5 Discussion . 171 Chapter 5: Fermionic Quivers . 176 5.1 Two-Node Fermionic Quivers . 178 5.2 Adjoint Dualities via Orbifolding . 183 5.3 Discussion and Further Work . 196 Chapter 6: Moving from 3d to 4d . 199 6.1 Deconstruction . 201 6.2 All-Scale Mirror Symetry . 207 6.3 S-duality from mirror symmetry . 213 6.4 Deconstruction with Abelian bosonization . 219 6.5 Discussion . 222 Appendix A: Review of Chern-Simons Theories . 224 Appendix B: 3d Bosonization Duality Supplementary . 228 B.1 Spin Considerations . 228 Appendix C: Flavor-Violated Master Duality Details . 231 Appendix D: Bosonic Quiver Supplementary . 236 D.1 Other Forms of the Duality . 236 D.2 Global Symmetries . 237 D.3 Bosonizing Interaction Terms . 240 D.4 Quivers and Spinc ................................. 246 Appendix E: Fermionic Quiver Supplementary . 248 E.1 Deriving Two-Node Fermionic Dualities . 248 E.2 Generalized Fermion Particle-Vortex Duality . 252 E.3 Two-Node Fermionic Quivers for the SO=Sp gauge group . 256 E.4 Gravitational Counterterm Matching . 257 Bibliography . 259 ii LIST OF FIGURES Figure Number Page 1.1 Mass deformed phases of Aharony's duality, (1.13a). .9 1.2 Various phases of the master duality and the non-Abelian reductions. The shaded red and blue correspond to the single-matter non-Abelian dualities. 20 2.1 Top: Mass deformation diagrams of the flavor-bounded 3d bosonization dual- ities of (1.13a) where Nf ≤ k. Here the blue and green lines are the RG flows of the respectively theories, and the black line is the mass deformation axis. Bottom: The flavor-violated extension of the usual 3d bosonization dualities proposed by [86]. Here we are working in the regime where k < Nf < N∗ and N > 2. The portion of the axis which is shaded yellow is the Grassmannian phase. The SU levels are without the additional −Nf =2 shift Ref. [86] (and many others) use to make things look more symmetric. We review the details of this diagram in Sec. 2.1. 25 2.2 Phase diagram of the flavor-bounded master duality with the labelling conven- tion used in Chapter 2 and Appendix C. Critical theories separating phases are the black lines. The dotted black lines represent a critical theory that would be present for N > Ns, but is not present for N = Ns......... 28 2.3 SU and U sides of the flavor-violated master duality for N > Ns. On the SU side, the critical lines in green are well-described by the corresponding SU theory. The critical lines in black are best described by the U duals. 31 2.4 SU and U sides of the flavor-violated master duality for N = Ns and jkj < Nf < N∗...................................... 36 4.1 Parent Chern-Simons matter theory at the phase transition for the special case n = 5. Nodes represent gauge theories with the associated Chern-Simons term and links represent matter bifundamentally charged under the gauge groups on the adjascent nodes. 108 iii 4.2 Derivation of the bosonic particle-vortex duality as a duality between two- node linear quiver theories. On the left-hand side, we have represented each side of Aharony's Abelian dualities as a two-node quiver. The filled yellow circle represents the color gauge group while the empty circle represents pro- moted global symmetries (which for the case of SU(1) are placeholders). The equation numbers corresponding to the two-node quivers are shown in red. Since the two fermionic theories are the same, one can perform a matching to arrive at a duality between three two-node quiver theories, the top and bottom of which are the XY and Abelian Higgs models, respectively. 110 4.3 Dualizing a linear quiver. Red nodes are SU gauge groups and black nodes are U groups. Black (red) links are bifundamental bosons (fermions). Applying Aharony's duality to the leftmost link turns the scalar into a fermion. Then, applying the master duality repeatedly moves said fermion across the quiver until it reaches the final link where Aharony's duality can again be used to turn the fermion into a boson. 117 4.4 Configuration of D6 branes. 143 4.5 Expected behavior of the vacuum energy as a function of θ in a large N gauge theory. Distinct branches are shown in different colors. 147 4.6 Flavored quiver with fermions on the SU side and scalars on the U side. The red/black nodes correspond to U and SU gauge groups, respectively. The red and black links are fermions and scalars. The white nodes are background flavor symmetries. 151 4.7 Flavored quiver with fermions on the SU side and scalars on the U side. This is an alternate theory in the flavor extended case. Here we have introduced the notation `i ≡ Fi − ki............................. 157 4.8 Explanation of interaction and enhanced flavor symmetries which arise due to the flavor-violated master duality and its finite interaction terms. We are using green/blue arrows to denote the (unidirectional) interactions. The green arrows represent finite interactions between the flavor degrees of freedom and adjacent bifundamentals. The light blue arrows represent interactions between bifundamental scalars, which were also present in the pure YM case of [8]. We assume they take the very same form they did there. The right-hand side shows how one arrives at enhanced flavor symmetries on the adjacent node at each step of the duality. 164 iv 5.1 Web of bosonization dualities in 2+1-dimensions. The contributions discussed in this chapter are shaded in red. Specifically, we show that the rank-two adjoint matter dualities can be connected to the rest of the web of dualities (red arrows). We also conjecture several new rank-two dualities including a duality with both fundamental and adjoint representation matter. 177 5.2 Generalized fermion quiver duality of (5.7) with flavor-bounded dualities. Theory B represents both Theories B' and B" since they are identical. Our quiver notation is such that we use filled red (black) nodes to represent dy- namical SU (U) gauge groups. The red (black) links between said circles represent fermions (scalars) charged under the corresponding gauge groups. This duality is subject to the flavor bound N2 = k1.............. 181 5.3 Generalized fermion quiver duality with flavor-violated bosonization duality. The first step uses the flavor-violated 3d bosonization duality, while the second step uses the flavor-bounded version. The diagram is valid for the k1 < N2 ≤ N∗(N2; k1); k2 < N1 ≤ N∗(N1; k2). ....................... 181 5.4 Phase diagram of the 3d bosonization duality with real adjoint matter [56]. Distinct theories are shown in different colors. The region shaded in purple corresponds to the quantum phase. 184 5.5 Phase diagram of the two-node quiver with explicit Z2 symmetry. Distinct theories are shown in different colors. Note the splitting of the bottom two phase diagrams which results from the use of the flavor-violated 3d bosoniza- tion duality. 186 5.6 Phase diagram for the novel real adjoint bosonization duality. 190 5.7 Phase diagram of the two-node quiver with extra flavors on each node and explicit Z2 symmetry. Here the white nodes represent global flavor symme- tries of the extra matter. Once more, the splitting of the bottom two phase diagrams results from the use of the flavor-violated 3d bosonization duality. We assume N > k and F < k.......................... 193 5.8 Phase diagram of the 3d bosonization duality with both adjoint and funda- mental representation matter.
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