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1. Non-planar corrections in ABJM theory from quantum M2 branes

   https://doi.org/10.1007/JHEP11(2024)056  

   Giombi, Simone; Kurlyand, Stefan A; Tseytlin, Arkady A (November 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> The quantization of semiclassical strings in AdS spacetimes yields predictions for the strong-coupling behaviour of the scaling dimensions of the corresponding operators in the planar limit of the dual gauge theory. Finding non-planar corrections requires computing string loops (corresponding to torus and higher genus surfaces), which is a challenging task. It turns out that in the case of theU_k(N) ×U_−k(N) ABJM theory there is an alternative approach: one may semiclassically quantize M2 branes in AdS₄×S⁷/ℤ_kwhich are wrapped around the 11d circle of radius 1/k=λ/N. Such M2 branes are the M-theory generalization of the strings in AdS × CP³. In this work, we show that by expanding in large M2 brane tensionT₂~$$ \sqrt{kN} $$ $\sqrt{\mathrm{kN}}$for fixedk, followed by an expansion in largek, we can predict the largeλasymptotics of the non-planar corrections to the dimensions of the dual ABJM operators. As a specific example, we consider the M2 brane configuration that generalizes the long folded string with large spin in AdS₄, and compute the 1-loop correction to its energy. This calculation allows us to determine non-planar corrections to the universal scaling function or cusp anomalous dimension. We extend our analysis to the semiclassical M2 branes that generalize the “short” and “long” circular strings with two equal angular momenta in CP³. The “short” M2 brane corresponds to a dual operator whose dimension at strong coupling scales as ∆ ∼λ^1/4+ …, and we derive the leading non-planar correction to it. 

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2. Fermions in AdS and Gross-Neveu BCFT

   https://doi.org/10.1007/JHEP07(2022)018  

   Giombi, Simone; Helfenberger, Elizabeth; Khanchandani, Himanshu (July 2022, Journal of High Energy Physics)

   A bstract We study the boundary critical behavior of conformal field theories of interacting fermions in the Gross-Neveu universality class. By a Weyl transformation, the problem can be studied by placing the CFT in an anti de Sitter space background. After reviewing some aspects of free fermion theories in AdS, we use both large N methods and the epsilon expansion near 2 and 4 dimensions to study the conformal boundary conditions in the Gross-Neveu CFT. At large N and general dimension d , we find three distinct boundary conformal phases. Near four dimensions, where the CFT is described by the Wilson-Fisher fixed point of the Gross-Neveu-Yukawa model, two of these phases correspond respectively to the choice of Neumann or Dirichlet boundary condition on the scalar field, while the third one corresponds to the case where the bulk scalar field acquires a classical expectation value. One may flow between these boundary critical points by suitable relevant boundary deformations. We compute the AdS free energy on each of them, and verify that its value is consistent with the boundary version of the F-theorem. We also compute some of the BCFT observables in these theories, including bulk two-point functions of scalar and fermions, and four-point functions of boundary fermions. 

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3. Monodromy defects from hyperbolic space

   https://doi.org/10.1007/JHEP02(2022)041  

   Giombi, Simone; Helfenberger, Elizabeth; Ji, Ziming; Khanchandani, Himanshu (February 2022, Journal of High Energy Physics)

   A bstract We study monodromy defects in O ( N ) symmetric scalar field theories in d dimensions. After a Weyl transformation, a monodromy defect may be described by placing the theory on S 1 × H d− 1 , where H d− 1 is the hyperbolic space, and imposing on the fundamental fields a twisted periodicity condition along S 1 . In this description, the codimension two defect lies at the boundary of H d− 1 . We first study the general monodromy defect in the free field theory, and then develop the large N expansion of the defect in the interacting theory, focusing for simplicity on the case of N complex fields with a one-parameter monodromy condition. We also use the ϵ -expansion in d = 4 − ϵ , providing a check on the large N approach. When the defect has spherical geometry, its expectation value is a meaningful quantity, and it may be obtained by computing the free energy of the twisted theory on S 1 × H d− 1 . It was conjectured that the logarithm of the defect expectation value, suitably multiplied by a dimension dependent sine factor, should decrease under a defect RG flow. We check this conjecture in our examples, both in the free and interacting case, by considering a defect RG flow that corresponds to imposing alternate boundary conditions on one of the low-lying Kaluza-Klein modes on H d− 1 . We also show that, adapting standard techniques from the AdS/CFT literature, the S 1 × H d− 1 setup is well suited to the calculation of the defect CFT data, and we discuss various examples, including one-point functions of bulk operators, scaling dimensions of defect operators, and four-point functions of operator insertions on the defect. 

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4. Dressing bulk fields in AdS3

   https://doi.org/10.1007/JHEP10(2020)189  

   Kabat, Daniel; Lifschytz, Gilad (October 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract We study a set of CFT operators suitable for reconstructing a charged bulk scalar field ϕ in AdS 3 (dual to an operator $$ \mathcal{O} $$ O of dimension ∆ in the CFT) in the presence of a conserved spin- n current in the CFT. One has to sum a tower of smeared non-primary scalars $$ {\partial}_{+}^m{J}^{(m)} $$ ∂ + m J m , where J ( m ) are primaries with twist ∆ and spin m built from $$ \mathcal{O} $$ O and the current. The coefficients of these operators can be fixed by demanding that bulk correlators are well-defined: with a simple ansatz this requirement allows us to calculate bulk correlators directly from the CFT. They are built from specific polynomials of the kinematic invariants up to a freedom to make field redefinitions. To order 1/ N this procedure captures the dressing of the bulk scalar field by a radial generalized Wilson line. 

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5. Exact SMEFT formulation and expansion to $$ \mathcal{O} $$(v4/Λ4)

   https://doi.org/10.1007/JHEP11(2020)087  

   Hays, Chris; Helset, Andreas; Martin, Adam; Trott, Michael (November 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract The Standard Model Effective Field Theory (SMEFT) theoretical framework is increasingly used to interpret particle physics measurements and constrain physics beyond the Standard Model. We investigate the truncation of the effective-operator expansion using the geometric formulation of the SMEFT, which allows exact solutions, up to mass-dimension eight. Using this construction, we compare the exact solution to the expansion at $$ \mathcal{O} $$ O ( v 2 / Λ 2 ), partial $$ \mathcal{O} $$ O ( v 4 / Λ 4 ) using a subset of terms with dimension-6 operators, and full $$ \mathcal{O} $$ O ( v 4 / Λ 4 ), where v is the vacuum expectation value and Λ is the scale of new physics. This comparison is performed for general values of the coefficients, and for the specific model of a heavy U(1) gauge field kinetically mixed with the Standard Model. We additionally determine the input-parameter scheme dependence at all orders in v/ Λ, and show that this dependence increases at higher orders in v/ Λ. 

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