118480483
Surface defects and instanton partition functions
A bstractWe study the superconformal index of five-dimensional SCFTs and the sphere partition function of four-dimensional gauge theories with eight supercharges in the presence of co-dimension two half-BPS defects. We derive a prescription which is valid for defects which can be given a “vortex construction”, i.e. can be defined by RG flow from vortex configurations in a larger theory. We test the prescription against known results and expected dualities. We employ our prescription to develop a general computational strategy for defects defined by coupling the bulk degrees of freedom to a Gauged Linear Sigma Model living in co-dimension two.
56423509
Defects and quantum Seiberg-Witten geometry
A bstractWe study the Nekrasov partition function of the five dimensional U(N) gauge theory with maximal supersymmetry on ℝ4 × S1 in the presence of codimension two defects. The codimension two defects can be described either as monodromy defects, or by coupling to a certain class of three dimensional quiver gauge theories on ℝ2 × S1. We explain how these computations are connected with both classical and quantum integrable systems. We check, as an expansion in the instanton number, that the aforementioned partition functions are eigenfunctions of an elliptic integrable many-body system, which quantizes the Seiberg-Witten geometry of the five-dimensional gauge theory.
119199828
The general M5-brane superconformal index
We calculate and study the general superconformal index for the 6d U(N) (2,0) theory with four chemical potentials, from the indices of gauge theories on CP^2 x R. Our index agrees with the large N supergravity index on AdS_7 x S^4 at low energies, and also yields the negative 'Casimir energy' with an N^3 scaling which was recently calculated from a QFT on S^5. Our approach also suggests a systematic study of the (1,0) superconformal indices.
118415614
On instantons as Kaluza-Klein modes of M5-branes
A bstractInstantons and W-bosons in 5d maximally supersymmetric Yang-Mills theory arise from a circle compactification of the 6d (2,0) theory as Kaluza-Klein modes and winding self-dual strings, respectively. We study an index which counts BPS instantons with electric charges in Coulomb and symmetric phases. We first prove the existence of unique threshold bound state of (noncommutative) U(1) instantons for any instanton number, and also show that charged instantons in the Coulomb phase correctly give the degeneracy of SU(2) self-dual strings. By studying SU(N) self-dual strings in the Coulomb phase, we find novel momentum-carrying degrees on the worldsheet. The total number of these degrees equals the anomaly coefficient of SU(N) (2,0) theory. We finally show that our index can be used to study the symmetric phase of this theory, and provide an interpretation as the superconformal index of the sigma model on instanton moduli space.
119259237
Schrödinger invariant solutions of M-theory with enhanced supersymmetry
We find the most general solution of 11-dimensional supergravity compatible with $ \mathcal{N} = 2 $ super-Schrödinger symmetry with six supercharges and $ {\text{SU}}(2) \times {\text{SU}}(2) \times {\text{U}}(1) \times {\mathbb{Z}_2} $ global symmetry. It can be viewed as a one-parameter extension of a recently constructed solution by Ooguri and Park. Our original motivation was to find the gravity dual of the non-relativistic ABJM theory. But, our analysis shows that no such solution exists within the reach of our assumptions. We discuss possible reasons for the non-existence of the desired solution. We also uplift a super-Schrödinger solution in IIB supergravity of Donos and Gauntlett to 11-dimension and comment on its properties.
118474061
Supersymmetric M5 brane theories on R × CP2
A bstractWe propose 4 and 12 supersymmetric conformal Yang-Mills-Chern-Simons theories on R × CP2 as multiple representations of the theory on M5 branes. These theories are obtained by twisted Zk modding and dimensional reduction of the 6d (2,0) superconformal field theory on R × S5 and have a discrete coupling constant $ \frac{1}{{g_{{Y\;M}}^2}}=\frac{k}{{4{\pi^2}}} $ with natural number k. Instantons in these theories are expected to represent the Kaluza-Klein modes. For the k = 1, 2 cases, we argue that the number of supersymmetries in our theories should be enhanced to 32 and 16, respectively. For the k = 3 case, only the 4 supersymmetric theory gets the supersymmetric enhancement to 8. For the 4 supersymmetric case, the vacuum structure becomes more complicated as there are degenerate supersymmetric vacua characterized by fuzzy spheres. We calculate the perturbative part of the SU(N ) gauge group Euclidean path integral for the index function at the symmetric phase of the 4 supersymmetric case and confirm it with the known half-BPS index. From the similar twisted Zk modding of the AdS7 × S4 geometry, we speculate that the M region is for k ≲ N1/3 and the type IIA region is N1/3 ≲ k ≲ N. When nonperturbative corrections are included, our theories are expected to produce the full index of the 6d (2,0) theory.
14029031
Hiding an extra dimension
We propose a new geometry and/or topology of a single extra dimension whose Kaluza-Klein excitations do appear at much higher scale than the inverse of the length/volume. For a single extra dimenion with volume Nπρ which is made of N intervals with size πρ attached at one point, Kaluza-Klein excitations can appear at 1/ρ rather than 1/Nρ which can hide the signal of the extra dimenion sufficiently for large N. The geometry considered here can be thought of a world volume theory of self intersecting branes or an effective description of complicated higher dimensional geometry such as Calabi-Yau with genus or multi-throat configurations. This opens a wide new domain of possible compactifications which deserves a serious investigation.
16451428
Gauge coupling renormalization in orbifold field theories
We investigate the gauge coupling renormalization in orbifold field theory preserving 4-dimensional N = 1 supersymmetry in the framework of 4-dimensional effective supergravity. As a concrete example, we consider the 5-dimensional Super-Yang-Mills theory on a slice of AdS5. In our approach, one-loop gauge couplings can be determined by the loop-induced axion couplings and the tree level properties of 4-dimensional effective supergravity which are much easier to be computed.
12889727
Criterion for admissible singularities in a brane world
When gravity couples to scalar fields in anti{endash}de Sitter (AdS) space, the geometry becomes non-AdS and develops singularities generally. We propose a criterion that the singularity is physically admissible if the integral of the on-shell Lagrangian density over the finite range is finite everywhere. For all classes of the singularities studied here, the criterion suggested in this paper coincides with an independent proposal made by Gubser that the potential should be bounded from above in the solution. This gives a reason why Gubser's conjecture works.
118390499
Beam–beam simulation code BBSIM for particle accelerators
A highly efficient, fully parallelized, six-dimensional tracking model for simulating interactions of colliding hadron beams in high energy ring colliders and simulating schemes for mitigating their effects is described. The model uses the weak-strong approximation for calculating the head-on interactions when the test beam has lower intensity than the other beam, a look-up table for the efficient calculation of long-range beam-beam forces, and a self-consistent Poisson solver when both beams have comparable intensities. A performance test of the model in a parallel environment is presented. The code is used to calculate beam emittance and beam loss in the Tevatron at Fermilab and compared with measurements. They also present results from the studies of stwo schemes proposed to compensate the beam-beam interactions: (a) the compensation of long-range interactions in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven and the Large Hadron Collider (LHC) at CERN with a current carrying wire, (b) the use of a low energy electron beam to compensate the head-on interactions in RHIC.
14019653
Top–bottom mass hierarchy, $s-\mu$ puzzle and gauge coupling unification with split multiplets
Abstract. Supersymmetric 5D SU(5) grand unification is considered. SU(5) is broken down to $G_{\mathrm{{SM}}}=SU(3)\times SU(2)\times U(1)$ by the $Z_2\times Z_2'$ assignment of the bulk field(s). The matter fields are located at the fixed point(s). In the bulk, a Higgs multiplet $\bar 5_H$ (containing the bottom doublet $H_1$) and the SU(5) gauge multiplet are located. At one fixed point, $H_2$ (the top doublet) and the standard model matter multiplets are presented. Because of the difference of the locations of $H_1$ and $H_2$, one can obtain a hierarchy between top and bottom Yukawa couplings. We also present a possible way to understand the s–$\mu$ mass puzzle in this framework of the split multiplet.