Higgs mediation with strong hidden sector dynamics

We present a simple model that achieves m h ≈ 126 GeV in the MSSM with large A -terms and TeV-scale stops through a combination of gauge mediation and Higgs-messenger interactions. The μ / B μ and A / m H 2 problems are both solved by a common mechanism — partial sequestering from strong hidden sector dynamics. Using the frame-work of General Messenger Higgs Mediation, we explicitly calculate the soft masses in terms of the vacuum expectation values, operator dimensions and OPE coefficients of the strongly-coupled hidden sector. Along the way, we also present a general analysis of the various constraints on sequestered Higgs mediation models. The phenomenology of such models is similar to gaugino mediation, but with large A -terms. The NLSP is always long-lived and is either the lightest stau or the Higgsino. The colored states are typically out of reach of the 8 TeV LHC, but may be accessible at 14 TeV, especially if the NLSP is the lightest stau

Classical conformal blocks and Painlevé VI

We study the classical c → ∞ limit of the Virasoro conformal blocks. We point out that the classical limit of the simplest nontrivial null-vector decoupling equation on a sphere leads to the Painlevé VI equation. This gives the explicit representation of generic four-point classical conformal block in terms of the regularized action evaluated on certain solution of the Painlevé VI equation. As a simple consequence, the monodromy problem of the Heun equation is related to the connection problem for the Painlevé VI

A swarm of B s

New physics signals containing five or more b -tagged jets, but without T or leptons, could realistically be sitting within the current 8 TeV LHC data set without receiving meaningful constraints from any of the existing LHC searches at either ATLAS or CMS. This work provides several examples of simple, motivated models that yield final states containing many b -jets. To study the potential for uncovering new physics in these high b -jet multiplicity channels, this paper focuses on a natural supersymmetry scenario where each of the pair-produced stops decays to an on-shell chargino, which subsequently decays via an MFV-motivated, R -parity violating coupling. This gives rise to an eight-jet final state containing six b -quarks. Although no public measurements exist, estimates indicate that the standard model backgrounds in high b -jet multiplicity channels should be very small. To circumvent the background uncertainty, an asymmetric method is presented that utilizes two different techniques to conservatively exclude or to discover new physics in high b -jet multiplicity final states

Toward full LHC coverage of natural supersymmetry

We argue that combining just a handful of searches for new physics at Run I of the LHC is sufficient to exclude most supersymmetric extensions of the Standard Model in which the gluino is kinematically accessible and the spectrum is natural. Such models typically give rise to significant T , top quarks and/or high object multiplicity, and we show that having even one of these signatures generally results in stringent limits. We also identify, among models that lack these signatures, the few gaps in coverage remaining, and propose search strategies to close these gaps. Our results are general and independent of the details of the spectrum, assumptions about minimality, R -parity, etc. Our analysis strategy should remain applicable when the LHC moves to higher energy. Central to our argument are ATLAS and CMS searches for many jets and low T , a proposed lepton + many jets search, an ATLAS search for 6-7 high- p T jets, and a reexamination of the control and signal regions of the CMS black hole search

S -duality and modular transformation as a non-perturbative deformation of the ordinary pq -duality

A recent claim that the S -duality between 4 d SUSY gauge theories, which is AGT related to the modular transformations of 2 d conformal blocks, is no more than an ordinary Fourier transform at the perturbative level, is further traced down to the commutation relation $\left[ {\mathop{P,}\limits^{\vee}\mathop{Q}\limits^{\vee }} \right]=-i\hbar$ between the check-operator monodromies of the exponential resolvent operator in the underlying Dotsenko-Fateev matrix models and β -ensembles. To this end, we treat the conformal blocks as eigenfunctions of the monodromy check operators, what is especially simple in the case of one-point toric block. The kernel of the modular transformation is then defined as the intertwiner of the two monodromies, and can be obtained straightforwardly, even when the eigenfunction interpretation of the blocks themselves is technically tedious. In this way, we provide an elementary derivation of the old expression for the modular kernel for the one-point toric conformal block

Integrable structure of Quantum Field Theory: classical flat connections versus quantum stationary states

We establish a correspondence between an infinite set of special solutions of the (classical) modified sinh-Gordon equation and a set of stationary states in the finite-volume Hilbert space of the integrable 2D QFT invented by V.A. Fateev. The modified sinh-Gordon equation arise in this case as a zero-curvature condition for a class of multivalued connections on the punctured Riemann sphere, similarly to Hitchin’s self-duality equations. The proposed correspondence between the classical and quantum integrable systems provides a powerful tool for deriving functional and integral equations which determine the full spectrum of local integrals of motion for massive QFT in a finite volume. Potential applications of our results to the problem of non-perturbative quantization of classically integrable non-linear sigma models are briefly discussed

Parameter counting for singular monopoles on ℝ 3

We compute the dimension of the moduli space of gauge-inequivalent solutions to the Bogomolny equation on ℝ 3 with prescribed singularities corresponding to the insertion of a finite number of ’t Hooft defects. We do this by generalizing the methods of C. Callias and E. Weinberg to the case of ℝ 3 with a finite set of points removed. For a special class of Cartan-valued backgrounds we go further and construct an explicit basis of ℒ 2 -normalizable zero-modes. Finally we exhibit and study a two-parameter family of spherically symmetric singular monopoles, using the dimension formula to provide a physical interpretation of these configurations. This paper is the first in a series of three on singular monopoles, where we also explore the role they play in the contexts of intersecting D-brane systems and four-dimensional N $$\mathcal{N}$$ =2 super Yang-Mills theories

Universal spectrum of 2d conformal field theory in the large c limit

Two-dimensional conformal field theories exhibit a universal free energy in the high temperature limit T → ∞, and a universal spectrum in the Cardy regime, Δ → ∞. We show that a much stronger form of universality holds in theories with a large central charge c and a sparse light spectrum. In these theories, the free energy is universal at all values of the temperature, and the microscopic spectrum matches the Cardy entropy for all Δ ≥ c 6 $$\Delta \ge \frac{c}{6}$$ . The same is true of three-dimensional quantum gravity; therefore our results provide simple necessary and sufficient criteria for 2d CFTs to behave holographically in terms of the leading spectrum and thermodynamics. We also discuss several applications to CFT and gravity, including operator dimension bounds derived from the modular bootstrap, universality in symmetric orbifolds, and the role of non-universal ‘enigma’ saddlepoints in the thermodynamics of 3d gravity

Brane bending and monopole moduli

We study intersecting brane systems that realize a class of singular monopole configurations in four-dimensional Yang-Mills-Higgs theory. Singular monopoles are solutions to the Bogomolny equation on ℝ 3 $${\mathrm{\mathbb{R}}}^3$$ with a prescribed number of singularities corresponding to the insertion of ’t Hooft defects. We use the brane construction to motivate a recent conjecture on the conditions for which the moduli space of solutions is non-empty. We also show how branes provide physical intuition for various aspects of the dimension formula derived in [1], including the contribution to the dimension from the defects and its invariance under Weyl reflections of the ’t Hooft charges. Along the way we uncover and illustrate new dynamical phenomena for the brane systems, including a description of smooth monopole extraction and bubbling from ’t Hooft defects

Topological strings and 5d T N partition functions

We evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5-branes, using the refined topological vertex on the dual Calabi-Yau three-folds. The theories include certain non-Lagrangian theories such as the T N theory. The refined topological vertex computation generically contains contributions from decoupled M2-branes which are not charged under the 5d gauge symmetry engineered. We argue that, after eliminating them, the refined topological string partition function agrees with the 5d Nekrasov partition function. We explicitly check this for the T 3 theory as well as Sp(1) gauge theories with N f = 2 , 3 , 4 flavors. In particular, our method leads to a new expression of the Sp(1) Nekrasov partition functions without any contour integrals. We also develop prescriptions to calculate the partition functions of theories obtained by Higgsing the T N theory. We compute the partition function of the E 7 theory via this prescription, and find the E 7 global symmetry enhancement. We finally discuss a potential application of the refined topological vertex to non-toric web diagrams