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Register a new userSymmetries in A-Type Little String Theories, Part I
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We analyse the symmetries of a class of A-type little string theories that are engineered by $N$ parallel M5-branes with M2-branes stretched between them. This paper deals with the so-called reduced free energy, which only receives contributions from the subset of the BPS states that carry the same charges under all the Cartan generators of the underlying gauge algebra. We argue (and check explicitly in a number of examples) that the former is invariant under the paramodular group $Sigma_Nsubset Sp(4,mathbb{Q})$, which gets extended to a subgroup of $Sp(4,mathbb{R})$ in the Nekrasov-Shatashvili-limit. This extension agrees with the observation made in arXiv:1706.04425 that these BPS states form a symmetric orbifold CFT. Furthermore, we argue that $Sigma_N$ (along with other symmetries) places strong constraints on the BPS counting function that governs the intersection between the M5- and M2-branes.
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We study a class of Little String Theories (LSTs) of A type, described by $N$ parallel M5-branes spread out on a circle and which in the low energy regime engineer supersymmetric gauge theories with $U(N)$ gauge group. The BPS states in this setting correspond to M2-branes stretched between the M5-branes. Generalising an observation made in arXiv:1706.04425, we provide evidence that the BPS counting functions of special subsectors of the latter exhibit a Hecke structure in the Nekrasov-Shatashvili (NS) limit, i.e. the different orders in an instanton expansion of the supersymmetric gauge theory are related through the action of Hecke operators. We extract $N$ distinct such reduced BPS counting functions from the full free energy of the LST with the help of contour integrals with respect to the gauge parameters of the $U(N)$ gauge group. Physically, the states captured by these functions correspond to configurations where the same number of M2-branes is stretched between some of these neighbouring M5-branes, while the remaining M5-branes are collapsed on top of each other and a particular singular contribution is extracted. The Hecke structures suggest that these BPS states form the spectra of symmetric orbifold CFTs. We furthermore show that to leading instanton order (in the NS-limit) the reduced BPS counting functions factorise into simpler building blocks. These building blocks are the expansion coefficients of the free energy for $N=1$ and the expansion of a particular function, which governs the counting of BPS states of a single M5-brane with single M2-branes ending on it on either side. To higher orders in the instanton expansion, we observe new elements appearing in this decomposition, whose coefficients are related through a holomorphic anomaly equation.
We revisit the N=6 superconformal Chern-Simons-matter theories and their supergravity duals in the context of generalized symmetries. This allows us to finally clarify how the $SU(N)times SU(N)$ and $(SU(N)times SU(N))/mathbb{Z}_N$ theories, as well as other quotient theories that have recently been discussed, fit into the holographic framework. It also resolves a long standing puzzle regarding the di-baryon operator in the $U(N)times U(N)$ theory.
We review the boundary state description of D-branes in type I string theory and show that the only stable non-BPS configurations are the D-particle and the D-instanton. We also compute the gauge and gravitational interactions of the non-BPS D-particles and compare them with the interactions of the dual non-BPS states of the heterotic string, finding complete agreement.
We study reductions of 6d theories on a $d$-dimensional manifold $M_d$, focusing on the interplay between symmetries, anomalies, and dynamics of the resulting $(6-d)$-dimensional theory $T[M_d]$. We refine and generalize the notion of polarization to polarization on $M_d$, which serves to fix the spectrum of local and extended operators in $T[M_d]$. Another important feature of theories $T[M_d]$ is that they often possess higher-group symmetries, such as 2-group and 3-group symmetries. We study the origin of such symmetries as well as physical implications including symmetry breaking and symmetry enhancement in the renormalization group flow. To better probe the IR physics, we also investigate the t Hooft anomaly of 5d Chern-Simons matter theories. The present paper focuses on developing the general framework as well as the special case of $d=0$ and 1, while an upcoming paper will discuss the case of $d=2$, $3$ and $4$.
We use the boundary state formalism to study, from the closed string point of view, superpositions of branes and anti-branes which are relevant in some non-perturbative string dualities. Treating the tachyon instability of these systems as proposed by A. Sen, we show how to incorporate the effects of the tachyon condensation directly in the boundary state. In this way we manage to show explicitly that the D1 -- anti-D1 pair of Type I is a stable non-BPS D-particle, and compute its mass. We also generalize this construction to describe other non-BPS D-branes of Type I. By requiring the absence of tachyons in the open string spectrum, we find which configurations are stable and compute their tensions. Our classification is in complete agreement with the results recently obtained using the K-theory of space-time.
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