Classical string solutions in Non-Relativistic AdS$_5\times$S$^5$: Closed and Twisted sectors

We find classical closed string solutions to the non-relativistic AdS$_5\times$S$^5$ string theory which are the analogue of the BMN and GKP solutions for the relativistic theory. We show that non-relativistic AdS$_5\times$S$^5$ string theory admits a $\mathbb{Z}_2$ orbifold symmetry which allows us to impose twisted boundary conditions. Among the solutions in the twisted sector, we find the one around which the semiclassical expansion in \href{https://arxiv.org/abs/2102.00008}{arXiv:2102.00008} takes place.

Lost chapters in CHL black holes: untwisted quarter-BPS dyons in the ℤ2 model

Motivated by recent advances in Donaldson-Thomas theory, four-dimensional $$ \mathcal{N} $$ N = 4 string-string duality is examined in a reduced rank theory on a less studied BPS sector. In particular we identify candidate partition functions of “untwisted” quarter-BPS dyons in the heterotic ℤ2 CHL model by studying the associated chiral genus two partition function, based on the M-theory lift of string webs argument by Dabholkar and Gaiotto. This yields meromorphic Siegel modular forms for the Iwahori subgroup B(2) ⊂ Sp4(ℤ) which generate BPS indices for dyons with untwisted sector electric charge, in contrast to twisted sector dyons counted by a multiplicative lift of twisted-twining elliptic genera known from Mathieu moonshine. The new partition functions are shown to satisfy the expected constraints coming from wall-crossing and S-duality symmetry as well as the black hole entropy based on the Gauss-Bonnet term in the effective action. In these aspects our analysis confirms and extends work of Banerjee, Sen and Srivastava, which only addressed a subset of the untwisted sector dyons considered here. Our results are also compared with recently conjectured formulae of Bryan and Oberdieck for the partition functions of primitive DT invariants of the CHL orbifold X = (K3 × T2)/ℤ2, as suggested by string duality with type IIA theory on X.

More non-Abelian mirrors and some two-dimensional dualities

In this paper, we extend the non-Abelian mirror proposal of two of the authors from two-dimensional gauge theories with connected gauge groups to the case of [Formula: see text] gauge groups with discrete theta angles. We check our proposed extension by counting and comparing vacua in mirrors to the known dual two-dimensional [Formula: see text] gauge theories. The mirrors in question are Landau–Ginzburg orbifolds, and for mirrors to [Formula: see text] gauge theories, the critical loci of the mirror superpotential often intersect fixed-point loci, so that to count vacua, one must take into account the twisted sector contributions. This is a technical novelty relative to the mirrors of gauge theories with connected gauge groups, for which critical loci do not intersect fixed-point loci and so no orbifold twisted sector contributions are pertinent. The vacuum computations turn out to be a rather intricate test of the proposed mirrors, in particular as untwisted sector states in the mirror to one theory are often exchanged with twisted sector states in the mirror to the dual. In cases with nontrivial IR limits, we also check that the central charges computed from the Landau–Ginzburg mirrors match those expected for the IR SCFTs.

THE ORBIFOLD-STRING THEORIES OF PERMUTATION-TYPE III: LORENTZIAN AND EUCLIDEAN SPACE—TIMES IN A LARGE EXAMPLE

To illustrate the general results of the previous paper, we discuss here a large concrete example of the orbifold-string theories of permutation-type. For each of the many subexamples, we focus on evaluation of the target space–time dimension[Formula: see text], the target space–time signature and the target space–time symmetry of each cycle j in each twisted sector σ. We find in particular a gratifying space–time symmetry enhancement which naturally matches the space–time symmetry of each cycle to its space–time dimension. Although the orbifolds of ℤ2-permutation-type are naturally Lorentzian, we find that the target space–times associated with larger permutation groups can be Lorentzian, Euclidean and even null [Formula: see text], with varying space–time dimensions, signature and symmetry in a single orbifold.

THE ORBIFOLD-STRING THEORIES OF PERMUTATION-TYPE II: CYCLE DYNAMICS AND TARGET SPACE–TIME DIMENSIONS

We continue our discussion of the general bosonic prototype of the new orbifold-string theories of permutation-type. Supplementing the extended physical-state conditions of the previous paper, we construct here the extended Virasoro generators with cycle central charge [Formula: see text], where fj(σ) is the length of cycle j in twisted sector σ. We also find an equivalent, reduced formulation of each physical-state problem at reduced cycle central charge cj(σ) = 26. These tools are used to begin the study of the target space–time dimension [Formula: see text] of cycle j in sector σ, which is naturally defined as the number of zero modes (momenta) of each cycle. The general model-dependent formulae derived here will be used extensively in succeeding papers, but are evaluated in this paper only for the simplest case of the "pure" permutation orbifolds.

An M-Theory Perspective on Heterotic K3 Orbifold Compactifications

We analyze the structure of heterotic M-theory on K3 orbifolds by presenting a comprehensive sequence of M-theoretic models constructed on the basis of local anomaly cancellation. This is facilitated by extending the technology developed in our previous papers to allow one to determine "twisted" sector states in nonprime orbifolds. These methods should naturally generalize to four-dimensional models, which are of potential phenomenological interest.