On TCS G2 manifolds and 4D emergent strings

Fengjun Xu

doi:10.1007/jhep10(2020)045

On TCS G2 manifolds and 4D emergent strings

Journal of High Energy Physics ◽

10.1007/jhep10(2020)045 ◽

2020 ◽

Vol 2020 (10) ◽

Author(s):

Fengjun Xu

Keyword(s):

Moduli Space ◽

Quantum Corrections ◽

Type Ii ◽

Quantum Level ◽

Weakly Coupled ◽

G2 Manifolds ◽

Fundamental Type ◽

M Theory ◽

Distance Limit ◽

Refined Version

Abstract In this note, we study the Swampland Distance Conjecture in TCS G2 manifold compactifications of M-theory. In particular, we are interested in testing a refined version — the Emergent String Conjecture, in settings with 4d N = 1 supersymmetry. We find that a weakly coupled, tensionless fundamental heterotic string does emerge at the infinite distance limit characterized by shrinking the K3-fiber in a TCS G2 manifold. Such a fundamental tensionless string leads to the parametrically leading infinite tower of asymptotically massless states, which is in line with the Emergent String Conjecture. The tensionless string, however, receives quantum corrections. We check that these quantum corrections do modify the volume of the shrinking K3-fiber via string duality and hence make the string regain a non-vanishing tension at the quantum level, leading to a decompactification. Geometrically, the quantum corrections modify the metric of the classical moduli space and are expected to obstruct the infinite distance limit. We also comment on another possible type of infinite distance limit in TCS G2 compactifications, which might lead to a weakly coupled fundamental type II string theory.

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Explicit soft supersymmetry breaking in the heterotic M-theory B − L MSSM

Journal of High Energy Physics ◽

10.1007/jhep08(2021)033 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Anthony Ashmore ◽

Sebastian Dumitru ◽

Burt A. Ovrut

Keyword(s):

Line Bundle ◽

Supersymmetry Breaking ◽

Moduli Space ◽

Initial Conditions ◽

Low Energy ◽

Strongly Coupled ◽

Hidden Sector ◽

Effective Lagrangian ◽

Soft Supersymmetry Breaking ◽

M Theory

Abstract The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the B − L MSSM theory is reviewed, including a discussion of the “bundle” constraints that both the observable sector SU(4) vector bundle and the hidden sector bundle induced from a single line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. The corresponding region of Kähler moduli space where all bundle constraints are satisfied is presented. The generic form of the moduli dependent F-terms due to a gaugino superpotential — which spontaneously break N = 1 supersymmetry in this sector — is presented and then given explicitly for the unique line bundle associated with the low condensation scale. The moduli-dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. We then show that at a large number of points in Kähler moduli space that satisfy all “bundle” constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term.

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6d (2, 0) and M-theory at 1-loop

Journal of High Energy Physics ◽

10.1007/jhep01(2021)133 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Luis F. Alday ◽

Shai M. Chester ◽

Himanshu Raj

Keyword(s):

Flat Space ◽

Lagrangian Description ◽

Loop Correction ◽

Higher Derivative ◽

Weakly Coupled ◽

S Matrix ◽

Space Limit ◽

Tensor Multiplet ◽

First Time ◽

M Theory

Abstract We study the stress tensor multiplet four-point function in the 6d maximally supersymmetric (2, 0) AN−1 and DN theories, which have no Lagrangian description, but in the large N limit are holographically dual to weakly coupled M-theory on AdS7× S4 and AdS7× S4/ℤ2, respectively. We use the analytic bootstrap to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity R and the first higher derivative correction R4 vertices, which is the first 1-loop correction computed for a non-Lagrangian theory. We then take the flat space limit and find precise agreement with the corresponding terms in the 11d M-theory S-matrix, some of which we compute for the first time using two-particle unitarity cuts.

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

Journal of High Energy Physics ◽

10.1007/jhep02(2021)139 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Eric D’Hoker ◽

Carlos R. Mafra ◽

Boris Pioline ◽

Oliver Schlotterer

Keyword(s):

Moduli Space ◽

Effective Interaction ◽

Type Ii ◽

Leading Order ◽

Effective Interactions ◽

Heterotic String Theory ◽

Genus Two ◽

Genus One ◽

Graph Function ◽

Point Amplitude

Abstract 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.

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Local G2-manifolds, Higgs bundles and a colored quantum mechanics

Journal of High Energy Physics ◽

10.1007/jhep05(2021)002 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Max Hübner

Keyword(s):

Quantum Mechanics ◽

Gauge Theories ◽

Supersymmetric Quantum Mechanics ◽

Higgs Bundle ◽

Higgs Bundles ◽

View Point ◽

Yang Mills ◽

G2 Manifolds ◽

Supersymmetric Gauge ◽

M Theory

Abstract M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

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Nothing is certain in string compactifications

Journal of High Energy Physics ◽

10.1007/jhep12(2020)032 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Iñaki García Etxebarria ◽

Miguel Montero ◽

Kepa Sousa ◽

Irene Valenzuela

Keyword(s):

Flux Compactifications ◽

Spin Structure ◽

Energy Condition ◽

Low Energy ◽

Type Ii ◽

String Compactifications ◽

Compact Dimension ◽

Bordism Group ◽

Topological Obstruction ◽

M Theory

Abstract A bubble of nothing is a spacetime instability where a compact dimension collapses. After nucleation, it expands at the speed of light, leaving “nothing” behind. We argue that the topological and dynamical mechanisms which could protect a compactification against decay to nothing seem to be absent in string compactifications once supersymmetry is broken. The topological obstruction lies in a bordism group and, surprisingly, it can disappear even for a SUSY-compatible spin structure. As a proof of principle, we construct an explicit bubble of nothing for a T3 with completely periodic (SUSY-compatible) spin structure in an Einstein dilaton Gauss-Bonnet theory, which arises in the low-energy limit of certain heterotic and type II flux compactifications. Without the topological protection, supersymmetric compactifications are purely stabilized by a Coleman-deLuccia mechanism, which relies on a certain local energy condition. This is violated in our example by the nonsupersymmetric GB term. In the presence of fluxes this energy condition gets modified and its violation might be related to the Weak Gravity Conjecture.We expect that our techniques can be used to construct a plethora of new bubbles of nothing in any setup where the low-energy bordism group vanishes, including type II compactifications on CY3, AdS flux compactifications on 5-manifolds, and M-theory on 7-manifolds. This lends further evidence to the conjecture that any non-supersymmetric vacuum of quantum gravity is ultimately unstable.

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Moduli spaces of non-geometric type II/heterotic dual pairs

Journal of High Energy Physics ◽

10.1007/jhep09(2020)082 ◽

2020 ◽

Vol 2020 (9) ◽

Author(s):

Yoan Gautier ◽

Dan Israël

Keyword(s):

Moduli Space ◽

Moduli Spaces ◽

Type Ii ◽

Duality Group ◽

Dual Pairs ◽

Perturbative Correction ◽

Singularity Structure ◽

Four Dimensions ◽

Geometric Type ◽

Perturbative Corrections

Abstract We study the moduli spaces of heterotic/type II dual pairs in four dimensions with $$ \mathcal{N} $$ N = 2 supersymmetry corresponding to non-geometric Calabi-Yau backgrounds on the type II side and to T-fold compactifications on the heterotic side. The vector multiplets moduli space receives perturbative corrections in the heterotic description only, and non- perturbative correction in both descriptions. We derive explicitely the perturbative corrections to the heterotic four-dimensional prepotential, using the knowledge of its singularity structure and of the heterotic perturbative duality group. We also derive the exact hypermultiplets moduli space, that receives corrections neither in the string coupling nor in α′.

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