Symplectic modular symmetry in heterotic string vacua: flavor, CP, and R-symmetries

We examine a common origin of four-dimensional flavor, CP, and U(1)R symmetries in the context of heterotic string theory with standard embedding. We find that flavor and U(1)R symmetries are unified into the Sp(2h + 2, ℂ) modular symmetries of Calabi-Yau threefolds with h being the number of moduli fields. Together with the $$ {\mathbb{Z}}_2^{\mathrm{CP}} $$ ℤ 2 CP CP symmetry, they are enhanced to GSp(2h + 2, ℂ) ≃ Sp(2h + 2, ℂ) ⋊ $$ {\mathbb{Z}}_2^{\mathrm{CP}} $$ ℤ 2 CP generalized symplectic modular symmetry. We exemplify the S3, S4, T′, S9 non-Abelian flavor symmetries on explicit toroidal orbifolds with and without resolutions and ℤ2, S4 flavor symmetries on three-parameter examples of Calabi-Yau threefolds. Thus, non-trivial flavor symmetries appear in not only the exact orbifold limit but also a certain class of Calabi-Yau three-folds. These flavor symmetries are further enlarged to non-Abelian discrete groups by the CP symmetry.

Hierarchical structure of physical Yukawa couplings from matter field Kähler metric

We study the impacts of matter field Kähler metric on physical Yukawa couplings in string compactifications. Since the Kähler metric is non-trivial in general, the kinetic mixing of matter fields opens a new avenue for realizing a hierarchical structure of physical Yukawa couplings, even when holomorphic Yukawa couplings have the trivial structure. The hierarchical Yukawa couplings are demonstrated by couplings of pure untwisted modes on toroidal orbifolds and their resolutions in the context of heterotic string theory with standard embedding. Also, we study the hierarchical couplings among untwisted and twisted modes on resolved orbifolds.

Phase transition at high supersymmetry breaking scale in heterotic string theory

When supersymmetry is spontaneously broken at the tree level, the spectrum of the heterotic string compactified on orbifolds of tori contains an infinite number of potentially tachyonic modes. We show that this implies instabilities of Minkowski space–time, when the scale of supersymmetry breaking is of the order of the string scale. We derive the phase space structure of vacua in the case where the tachyonic spectrum contains a mode with trivial momenta and winding numbers along the internal directions not involved in the supersymmetry breaking.

Two-loop superstring five-point amplitudes. Part II. Low energy expansion and S-duality

In an earlier paper, we constructed the genus-two amplitudes for five external massless states in Type II and Heterotic string theory, and showed that the α′ expansion of the Type II amplitude reproduces the corresponding supergravity amplitude to leading order. In this paper, we analyze the effective interactions induced by Type IIB superstrings beyond supergravity, both for U(1)R-preserving amplitudes such as for five gravitons, and for U(1)R-violating amplitudes such as for one dilaton and four gravitons. At each order in α′, the coefficients of the effective interactions are given by integrals over moduli space of genus-two modular graph functions, generalizing those already encountered for four external massless states. To leading and sub-leading orders, the coefficients of the effective interactions D2ℛ5 and D4ℛ5 are found to match those of D4ℛ4 and D6ℛ4, respectively, as required by non-linear supersymmetry. To the next order, a D6ℛ5 effective interaction arises, which is independent of the supersymmetric completion of D8ℛ4, and already arose at genus one. A novel identity on genus-two modular graph functions, which we prove, ensures that up to order D6ℛ5, the five-point amplitudes require only a single new modular graph function in addition to those needed for the four-point amplitude. We check that the supergravity limit of U(1)R-violating amplitudes is free of UV divergences to this order, consistently with the known structure of divergences in Type IIB supergravity. Our results give strong consistency tests on the full five-point amplitude, and pave the way for understanding S-duality beyond the BPS-protected sector.

Implications of Einstein–Maxwell dilaton–axion gravity from the black hole continuum spectrum

ABSTRACT String inspired models can serve as potential candidates to replace general relativity (GR) in the high-energy/high-curvature regime where quantum gravity is expected to play a vital role. Such models not only subsume the ultraviolet nature of gravity but also exhibit promising prospects in resolving issues like dark matter and dark energy, which cannot be adequately addressed within the framework of GR. The Einstein–Maxwell dilaton–axion (EMDA) theory that is central to this work is one such string inspired model arising in the low energy effective action of the heterotic string theory with interesting implications in inflationary cosmology and in the late-time acceleration of the Universe. It is therefore important to survey the role of such a theory in explaining astrophysical observations, e.g. the continuum spectrum of black holes which is expected to hold a wealth of information regarding the background metric. The Kerr–Sen space–time corresponds to the exact, stationary, and axisymmetric black hole solution in EMDA gravity, possessing dilatonic charge and angular momentum originating from the axionic field. In this work, we compute the theoretical spectrum from the accretion disc around quasars in the Kerr–Sen background assuming the thin accretion disc model due to Novikov and Thorne. This is then used to evaluate the theoretical estimates of optical luminosity for a sample of eighty Palomar Green quasars which are subsequently compared with the available observations. Our results based on χ2 analysis indicate that the dilaton parameter r2 ∼ 0.2 is favoured by optical observations of quasars which is further corroborated by other error estimators e.g. the Nash–Sutcliffe efficiency, the index of agreement and their modified versions. We further report that strong dilaton charges (r2 > 1.6) are disfavoured by quasar optical data and the spins associated with the quasars are also estimated.

Kerr–Sen–Taub–NUT spacetime and circular geodesics

We present a solution obeying classical equation of motion in the low energy limit of heterotic string theory. The solution represents a rotating mass with electric charge and gravitomagnetic monopole moment. The corresponding conserved charges are discussed, and the separability of Hamilton–Jacobi equation for a test body in the spacetime is also investigated. Some numerical results related to the circular motions on equatorial plane are presented, but there is none that supports the existence of such geodesics.

F-theory and heterotic duality, Weierstrass models from Wilson lines

We present how to construct elliptically fibered K3 surfaces via Weierstrass models which can be parametrized in terms of Wilson lines in the dual heterotic string theory. We work with a subset of reflexive polyhedras that admit two fibers whose moduli spaces contain the ones of the $$E_{8}\times E_{8}$$ E 8 × E 8 or $$\frac{Spin(32)}{{\mathbb {Z}}_{2}}$$ S p i n ( 32 ) Z 2 heterotic theory compactified on a two torus without Wilson lines. One can then interpret the additional moduli as a particular Wilson line content in the heterotic strings. A convenient way to find such polytopes is to use graphs of polytopes where links are related to inclusion relations of moduli spaces of different fibers. We are then able to map monomials in the defining equations of particular K3 surfaces to Wilson line moduli in the dual theories. Graphs were constructed developing three different programs which give the gauge group for a generic point in the moduli space, the Weierstrass model as well as basic enhancements of the gauge group obtained by sending coefficients of the hypersurface equation defining the K3 surface to zero.

Shadows of charged rotating black holes: Kerr–Newman versus Kerr–Sen

Celebrating the centennial of its first experimental test, the theory of General Relativity (GR) has successfully and consistently passed all subsequent tests with flying colors. It is expected, however, that at certain scales new physics, in particular, in the form of quantum corrections, will emerge, changing some of the predictions of GR, which is a classical theory. In this respect, black holes (BHs) are natural configurations to explore the quantum effects on strong gravitational fields. BH solutions in the low-energy effective field theory description of the heterotic string theory, which is one of the leading candidates to describe quantum gravity, have been the focus of many studies in the last three decades. The recent interest in strong gravitational lensing by BHs, in the wake of the Event Horizon Telescope (EHT) observations, suggests comparing the BH lensing in both GR and heterotic string theory, in order to assess the phenomenological differences between these models. In this work, we investigate the differences in the shadows of two charged BH solutions with rotation: one arising in the context of GR, namely the Kerr–Newman (KN) solution, and the other within the context of low-energy heterotic string theory, the Kerr–Sen (KS) solution. We show and interpret, in particular, that the stringy BH always has a larger shadow, for the same physical parameters and observation conditions.

Critical behavior of AdS Gauss–Bonnet massive black holes in the presence of external string cloud

Following previous study about AdS-Schwarzschild black holes minimally coupled to a cloud of strings in the context of massive gravity (Ghanaatian et al. in Effects of the external string cloud on the Van der Waals like behavior and efficiency of AdS-Schwarzschild black hole in massive gravity, arXiv:1906.00369 [hep-th]) and inspired by strong connection between Gauss–Bonnet Gravity and heterotic string theory, in this paper, we first take into account the Gauss–Bonnet term and we study thermodynamics and critical behavior of these black holes in the extended phase space. The effects of Gauss–Bonnet, massive, and string cloud parameters on the criticality of these black holes has been investigated. It can be seen that the Gauss–Bonnet and massive parameters have opposite effects on the criticality and phase transition of the solutions. We also observe that the increase in the value of the string cloud parameter above a critical value, eliminates the van der Waals like behavior of these solutions. Also, the Joule–Thomson effect is not observed. Then we examine thermal stability of these black holes in canonical ensemble by calculating the heat capacity. In addition, we explore critical behavior in extended phase space by employing heat capacity and consequently, we observe that the results are in agreement with the previous results from the usual method in Sect. 3.