摘要 :
The superconformal index of quiver gauge theories realized on D3-branes in toric Calabi–Yau cones is investigated. We use the AdS/CFT correspondence and study D3-branes wrapped on supersymmetric cycles. We focus on brane configur...
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The superconformal index of quiver gauge theories realized on D3-branes in toric Calabi–Yau cones is investigated. We use the AdS/CFT correspondence and study D3-branes wrapped on supersymmetric cycles. We focus on brane configurations in which a single D3-brane is wrapped on a cycle, and we do not take account of branes with multiple wrapping. We propose a formula that gives finite-|$N$| corrections to the index caused by such brane configurations. We compare the predictions of the formula for several examples with the results on the gauge theory side obtained by using localization for small sizes of gauge groups, and confirm that the formula correctly reproduces the finite-|$N$| corrections up to the expected order.
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摘要 :
In the leading order of the large-|$N$| approximation, we study the renormalon ambiguity in the gluon (or, more appropriately, photon) condensate in the 2D supersymmetric |$\mathbb{C}P^{N-1}$| model on |$\mathbb{R}\times S^1$| wit...
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In the leading order of the large-|$N$| approximation, we study the renormalon ambiguity in the gluon (or, more appropriately, photon) condensate in the 2D supersymmetric |$\mathbb{C}P^{N-1}$| model on |$\mathbb{R}\times S^1$| with the |$\mathbb{Z}_N$| twisted boundary conditions. In our large-|$N$| limit, the combination |$\Lambda R$|?, where |$\Lambda$| is the dynamical scale and |$R$| is the |$S^1$| radius, is kept fixed (we set |$\Lambda R\ll1$| so that the perturbative expansion with respect to the coupling constant at the mass scale |$1/R$| is meaningful). We extract the perturbative part from the large-|$N$| expression of the gluon condensate and obtain the corresponding Borel transform |$B(u)$|?. For |$\mathbb{R}\times S^1$|?, we find that the Borel singularity at |$u=2$|?, which exists in the system on the uncompactified |$\mathbb{R}^2$| and corresponds to twice the minimal bion action, disappears. Instead, an unfamiliar renormalon singularity emerges at |$u=3/2$| for the compactified space |$\mathbb{R}\times S^1$|?. The semi-classical interpretation of this peculiar singularity is not clear because |$u=3/2$| is not dividable by the minimal bion action. It appears that our observation for the system on |$\mathbb{R}\times S^1$| prompts reconsideration on the semi-classical bion picture of the infrared renormalon.
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摘要 :
By employing the |$1/N$| expansion, we compute the vacuum energy |$E(\delta\epsilon)$| of the two-dimensional supersymmetric (SUSY) |$\mathbb{C}P^{N-1}$| model on |$\mathbb{R}\times S^1$| with |$\mathbb{Z}_N$| twisted boundary con...
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By employing the |$1/N$| expansion, we compute the vacuum energy |$E(\delta\epsilon)$| of the two-dimensional supersymmetric (SUSY) |$\mathbb{C}P^{N-1}$| model on |$\mathbb{R}\times S^1$| with |$\mathbb{Z}_N$| twisted boundary conditions to the second order in a SUSY-breaking parameter |$\delta\epsilon$|?. This quantity was vigorously studied recently by Fujimori et al. using a semi-classical approximation based on the bion, motivated by a possible semi-classical picture on the infrared renormalon. In our calculation, we find that the parameter |$\delta\epsilon$| receives renormalization and, after this renormalization, the vacuum energy becomes ultraviolet finite. To the next-to-leading order of the |$1/N$| expansion, we find that the vacuum energy normalized by the radius of the |$S^1$|?, |$R$|?, |$RE(\delta\epsilon)$| behaves as inverse powers of |$\Lambda R$| for |$\Lambda R$| small, where |$\Lambda$| is the dynamical scale. Since |$\Lambda$| is related to the renormalized ’t Hooft coupling |$\lambda_R$| as |$\Lambda\sim e^{-2\pi/\lambda_R}$|?, to the order of the |$1/N$| expansion we work out, the vacuum energy is a purely non-perturbative quantity and has no well-defined weak coupling expansion in |$\lambda_R$|?.
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Grand gauge-Higgs unification of 5D |$SU(6)$| gauge theory on an orbifold |$S^1/Z_2$| is discussed. The Standard Model (SM) fermions are introduced on one of the boundaries and some massive bulk fields are also introduced so that ...
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Grand gauge-Higgs unification of 5D |$SU(6)$| gauge theory on an orbifold |$S^1/Z_2$| is discussed. The Standard Model (SM) fermions are introduced on one of the boundaries and some massive bulk fields are also introduced so that they couple to the SM fermions through the mass terms on the boundary. Integrating out the bulk fields generates SM fermion masses with exponentially small bulk mass dependences. The SM fermion masses except for the top quark are shown to be reproduced by mild tuning of the bulk masses. The one-loop Higgs potential is calculated and it is shown that electroweak symmetry breaking occurs by introducing additional bulk fields. The Higgs boson mass is also computed.
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We propose a minimal and self-contained model in non-compact flat five dimensions that localizes the Standard Model (SM) on a domain wall. Localization of gauge fields is achieved by condensation of the Higgs field via a Higgs-dep...
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We propose a minimal and self-contained model in non-compact flat five dimensions that localizes the Standard Model (SM) on a domain wall. Localization of gauge fields is achieved by condensation of the Higgs field via a Higgs-dependent gauge kinetic term in the 5D Lagrangian. The domain wall connecting vacua with unbroken gauge symmetry drives the Higgs condensation, which provides both electroweak symmetry breaking and gauge field localization at the same time. Our model predicts higher-dimensional interactions |$|H|^{2n}(F_{\mu\nu})^2$| in the low-energy effective theory. This leads to two expectations: One is a new tree-level contribution to |$H \to \gamma\gamma$| (?|$H \to gg$|?) decay whose signature will be testable in future LHC experiments. The other is a finite electroweak monopole that may be accessible to the MoEDAL experiment. Interactions of the translational Nambu–Goldstone boson are shown to satisfy a low-energy theorem.
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We present a flavor model with |$S_3$| modular invariance in the framework of SU(5) grand unified theory (GUT). The |$S_3$| modular forms of weights |$2$| and |$4$| give the quark and lepton mass matrices with a common complex par...
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We present a flavor model with |$S_3$| modular invariance in the framework of SU(5) grand unified theory (GUT). The |$S_3$| modular forms of weights |$2$| and |$4$| give the quark and lepton mass matrices with a common complex parameter, the modulus |$\tau$|?. The GUT relation of down-type quarks and charged leptons is imposed by the vacuum expectation value (VEV) of the adjoint 24-dimensional Higgs multiplet in addition to the VEVs of |$5$| and |$\bar 5$| Higgs multiplets of SU(5). The observed Cabibbo–Kobayashi–Maskawa and Pontecorvo–Maki–Nakagawa–Sakata mixing parameters as well as the mass eigenvalues are reproduced properly. We discuss the leptonic charge–parity phase and the effective mass of the neutrinoless double beta decay with the sum of neutrino masses.
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摘要 :
We study the superconformal index of S-fold theories by using the anti-de Sitter / conformal field theory correspondence. It is known that the index in the large-|$N$| limit is reproduced as the contribution of bulk Kaluza–Klein ...
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We study the superconformal index of S-fold theories by using the anti-de Sitter / conformal field theory correspondence. It is known that the index in the large-|$N$| limit is reproduced as the contribution of bulk Kaluza–Klein modes. For finite-|$N$|?, D3-branes wrapped around the non-trivial cycle in |$\boldsymbol{S}^5/\mathbb{Z}_k$|?, which corresponds to Pfaffian-like operators, give the corrections of order |$q^N$| to the index. We calculate the finite-|$N$| corrections by analyzing the fluctuations of wrapped D3-branes. Comparisons to known results show that our formula correctly reproduces the corrections up to errors of order |$q^{2N}$|?.
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We show that the massless form fields in |$(4+1)$|-dimensional non-perturbation theory of emergent gravity become massive in a perturbative phase without the Higgs mechanism. In particular, an axionic scalar sourced by a non-pertu...
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We show that the massless form fields in |$(4+1)$|-dimensional non-perturbation theory of emergent gravity become massive in a perturbative phase without the Higgs mechanism. In particular, an axionic scalar sourced by a non-perturbative dynamical correction is absorbed by the form fields to describe a massive Neveu–Schwarz (NS) field theory on an emergent gravitational |$(3{\bar 3})$|-brane pair. Arguably the novel idea of the Higgs mechanism is naturally invoked in an emergent gravity underlying a |${\rm CFT}_6$|?. Analysis reveals “gravito-weak” and “electro-weak” phases respectively on a vacuum pair in |$(4+1)$| and |$(3+1)$| dimensions. It is argued that the massive NS field quanta may govern an emergent graviton on a gravitational |$3$|-brane.
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Gauge/gravity correspondence is regarded as a powerful tool for the study of strongly coupled quantum systems, but its proof is not available. An unresolved issue that should be closely related to the proof is what kind of corresp...
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Gauge/gravity correspondence is regarded as a powerful tool for the study of strongly coupled quantum systems, but its proof is not available. An unresolved issue that should be closely related to the proof is what kind of correspondence exists, if any, when gauge theory is weakly coupled. We report progress about this limit for the case associated with D|$p$|-branes (?|$0\le p\le 4$|?), namely, the duality between the |$(p+1)$|D maximally supersymmetric Yang–Mills theory and superstring theory on the near-horizon limit of the D|$p$|-brane solution. It has been suggested by supergravity analysis that the two-point functions of certain operators in gauge theory obey a power law with the power different from the free-field value for |$p\neq 3$|?. In this work, we show for the first time that the free-field result can be reproduced by superstring theory on the strongly curved background. The operator that we consider is of the form |${\rm Tr}(Z^J)$|?, where |$Z$| is a complex combination of two scalar fields. We assume that the corresponding string has the worldsheet spatial direction discretized into |$J$| bits, and use the fact that these bits become non-interacting when ’t Hooft coupling is zero.
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BPS vortex systems on closed Riemann surfaces with arbitrary genus are embedded into 2D supersymmetric Yang–Mills theory with matters. We turn on background |$R$|-gauge fields to keep half of the rigid supersymmetry (topological ...
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BPS vortex systems on closed Riemann surfaces with arbitrary genus are embedded into 2D supersymmetric Yang–Mills theory with matters. We turn on background |$R$|-gauge fields to keep half of the rigid supersymmetry (topological A-twist) on the curved space. We consider two complementary descriptions: Higgs and Coulomb branches. The path integral reduces to the zero mode integral by the localization in the Higgs branch. The integral over the bosonic zero modes directly gives an integral over the volume form of the moduli space, whereas the fermionic zero modes are compensated by an appropriate operator insertion. In the Coulomb branch description with the same operator insertion, the path integral reduces to a finite-dimensional residue integral. The operator insertion automatically determines a choice of integral contours, leading to the Jeffrey–Kirwan residue formula. This result ensures the existence of the solution to the BPS vortex equation and explains the Bradlow bounds of the BPS vortex. We also discuss a generating function of the volume of the vortex moduli space and show a reduction of the moduli space from semi-local to local vortices.
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