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We study generalized (doubled) structures in 2 D -dimensional Born geometries in which T-duality symmetry is manifestly realized. We show that spacetime structures of Kähler, hyperkähler, bi-hermitian and bi-hypercomplex manifolds are implemented in Born geometries as generalized (doubled) structures. We find that the Born structures and the generalized Kähler (hyperkähler) structures appear as subalgebras of bi-quaternions ℂ × ℍ and split-tetra-quaternions ℍ × Spℍ. We investigate the nature of T-duality for the worldsheet instantons in Born sigma models. This manuscript is based on the original paper [1].

We investigate the T-duality relations between hyperkähler and bi-hypercomplex structures using the doubled formalism. In generalized geometry, both the hyperkähler and bi-hypercomplex structures are embedded in generalized hyperkähler structures that satisfy the split-bi-quaternion algebra. We write down the analogue of the Buscher rule, which is the T-duality transformation of the hyperkähler and bi-hypercomplex structures. As a practical example, we construct the bi-hypercomplex structure of the 5 2 2 -brane, known as a T-fold, from the hyperkähler structure of the Taub-NUT space using the T-duality transformation. The bi-hypercomplex structures of the T-fold have non-trivial monodromies. This results in the fact that the worldsheet instantons on the T-fold are multi-valued. We comment on the resolution of this issue using the Born sigma model.

A bstract We consider the SU( N ) Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of p . We can formulate such a quantum field theory maintaining locality and unitarity, and the model contains both 2 π -periodic scalar and 3-form gauge fields. This can be interpreted as coupling a topological theory to Yang-Mills theory, so the local dynamics becomes identical with that of pure Yang-Mills theory. The theory has not only ℤ N 1-form symmetry but also ℤ p 3-form symmetry, and we study the global nature of this theory from the recent ’t Hooft anomaly matching. The computation of ’t Hooft anomaly incorporates an intriguing higher-group structure. We also carefully examine that how such kinematical constraint is realized in the dynamics by using the large- N and also the reliable semiclassics on ℝ 3 × S 1 , and we find that the topological susceptibility plays a role of the order parameter for the ℤ p 3-form symmetry. Introducing a fermion in the fundamental or adjoint representation, we find that the chiral symmetry becomes larger than the usual case by ℤ p , and it leads to the extra p vacua by discrete chiral symmetry breaking. No dynamical domain wall can interpolate those extra vacua since such objects must be charged under the 3-form symmetry in order to match the ’t Hooft anomaly.

There are two distinct regimes of Yang-Mills theory where we can demonstrate confinement, the existence of a mass gap, and the multi-branch structure of the effective potential as a function of the theta angle using a reliable semi-classical calculation. The two regimes are deformed Yang-Mills theory on ℝ3 × S1, and Yang-Mills theory on ℝ2 × T2 where the torus is threaded by a ’t Hooft flux. The weak coupling regime is ensured by the small size of the circle or torus. In the first case the confinement mechanism is related to self-dual monopoles, whereas in the second case self-dual center-vortices play a crucial role. These two topological objects are distinct. In particular, they have different mutual statistics with Wilson loops. On the other hand, they carry the same topological charge and action. We consider the theory on ℝ × T2 × S1 and extrapolate both the monopole and vortex regimes to a quantum mechanical domain, where a cross-over takes place. Both sides of the cross-over are described by a deformed ℤN TQFT. On ℝ2 × S1 × S1, we derive an effective field theory (EFT) of vortices from the EFT of monopoles in the presence of a ’t Hooft flux. This construction is based on a two-stage Higgs mechanism, reducing SU(N) to U(1)N−1 in 3d first, followed by reduction to a ℤN EFT in 2d in the second step. This result shows how monopoles transmute into center-vortices, and suggests adiabatic continuity between the two confinement mechanisms. The basic mechanism is flux fractionalization: the magnetic flux of the monopoles splits up and is collimated in such a way that 2d Wilson loops detect it as a center vortex.

A bstract We consider the strong dynamics associated with a composite Higgs model that simultaneously produces dynamical axions and solves the strong CP problem. The strong dynamics arises from a new Sp or SU(4) hypercolor gauge group containing QCD colored hyperfermions that confines at a high scale. The hypercolor global symmetry is weakly gauged by the Standard Model electroweak gauge group and an enlarged color group, SU( N + 3) × SU( N ) ′ . When hyperfermion condensates form, they not only lead to an SU(5)/SO(5) composite Higgs model but also spontaneously break the enlarged color group to SU(3) c × SU( N ) D . At lower energies, the SU( N ) D group confines, producing two dynamical axions that eliminates all CP violation. Furthermore, small instantons from the SU( N ) ′ group can enhance the axion mass, giving rise to TeV scale axion masses that can be detected at collider experiments. Our model provides a way to unify the composite Higgs with dynamical axions, without introducing new elementary scalar fields, while also extending the range of axion masses that addresses the strong CP problem.

A bstract We calculate a new contribution to the axion mass that arises from gluons propagating in a 5th dimension at high energies. By uplifting the 4D instanton solution to five dimensions, the positive frequency modes of the Kaluza-Klein states generate a power-law term in the effective action that inversely grows with the instanton size. This causes 5D small instantons to enhance the axion mass in a way that does not spoil the axion solution to the strong CP problem. Moreover this enhancement can be much larger than the usual QCD contribution from large instantons, although it requires the 5D gauge theory to be near the non-perturbative limit. Thus our result suggests that the mass range of axions (or axion-like particles), which is important for ongoing experimental searches, can depend sensitively on the UV modification of QCD.

A bstract We study the vacuum pair production by a time-dependent strong electric field based on the exact WKB analysis. We identify the generic structure of a Stokes graph for systems with the vacuum pair production and show that the number of produced pairs is given by a product of connection matrices for Stokes segments connecting pairs of turning points. We derive an explicit formula for the number of produced pairs, assuming the semi-classical limit. The obtained formula can be understood as a generalization of the divergent asymptotic series method by Berry, and is consistent with other semi-classical methods such as the worldline instanton method and the steepest descent evaluation of the Bogoliubov coefficients done by Brezin and Izykson. We also use the formula to discuss effects of time-dependence of the applied strong electric field including the interplay between the perturbative multi-photon pair production and non-peturbative Schwinger mechanism, and the dynamically assisted Schwinger mechanism.

A bstract We examine the contribution of small instantons to the axion mass in various UV completions of QCD. We show that the reason behind the potential dominance of such contributions is the non-trivial embedding of QCD into the UV theory. The effects from instantons in the partially broken gauge group appear as “fractional instanton” corrections in the effective theory. These will exhibit unusual dependences on the various scales in the problem whenever the index of embedding is non-trivial. We present a full one-instanton calculation of the axion mass in the simplest product group models, carefully keeping track of numerical prefactors. Rather than using a ’t Hooft operator approximation we directly evaluate the contributions to the vacuum bubble, automatically capturing the effects of closing up external fermion lines with Higgs loops. This approach is manifestly finite and removes the uncertainty associated with introducing a cutoff scale for the Higgs loops. We verify that the small instantons may dominate over the QCD contribution for very high breaking scales and at least three group factors.

A bstract We establish that unitarity of scattering amplitudes imposes universal entropy bounds. The maximal entropy of a self-sustained quantum field object of radius R is equal to its surface area and at the same time to the inverse running coupling α evaluated at the scale R . The saturation of these entropy bounds is in one-to-one correspondence with the non-perturbative saturation of unitarity by 2 → N particle scattering amplitudes at the point of optimal truncation. These bounds are more stringent than Bekenstein’s bound and in a consistent theory all three get saturated simultaneously. This is true for all known entropy-saturating objects such as solitons, instantons, baryons, oscillons, black holes or simply lumps of classical fields. We refer to these collectively as saturons and show that in renormalizable theories they behave in all other respects like black holes. Finally, it is argued that the confinement in SU( N ) gauge theory can be understood as a direct consequence of the entropy bounds and unitarity.

A bstract We consider general 5d SU( N ) quiver gauge theories whose nodes form an ADE Dynkin diagram of type G . Each node has SU( N i ) gauge group of general rank, Chern-Simons level κ i and additional w i fundamentals. When the total flavor number at each node is less than or equal to 2 N i − 2| κ i |, we give general rules under which the symmetries associated to instanton currents are enhanced to G × G or a subgroup of it in the UV 5d superconformal theory. When the total flavor number violates that condition at some of the nodes, further enhancement of flavor symmetries occurs. In particular we find a large class of gauge theories interpreted as S 1 compactification of 6d superconformal theories which are waiting for string/F-theory realization. We also consider hypermultiplets in (anti-)symmetric representation.