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Extracting reliable low-energy information from string compactifications notoriously requires a detailed understanding of the UV sensitivity of the corresponding effective field theories. Despite past efforts in computing perturbative string corrections to the tree-level action, neither a systematic approach nor a unified framework has emerged yet. We make progress in this direction, focusing on the moduli dependence of perturbative corrections to the 4D scalar potential of type IIB Calabi-Yau orientifold compactifications. We proceed by employing two strategies. First, we use two rescaling symmetries of type IIB string theory to infer the dependence of any perturbative correction on both the dilaton and the Calabi-Yau volume. Second, we use F/M-theory duality to conclude that KK reductions on elliptically-fibred Calabi-Yau fourfolds of the M-theory action at any order in the derivative expansion can only generate $(\alpha')^{\rm even}$ corrections to the 4D scalar potential, which, moreover, all vanish for trivial fibrations. We finally give evidence that $(\alpha')^{\rm odd}$ effects arise from integrating out KK and winding modes on the elliptic fibration and argue that the leading no-scale breaking effects at string tree-level arise from $(\alpha')^3$ effects, modulo potential logarithmic corrections., Comment: 36 pages plus appendices, 4 figures

We study T-branes on compact Kaehler surfaces, in the presence of fields localised at curves. If such fields are treated as defects, their vevs induce delta-function sources for the 7-brane background, possibly leading to profiles with poles. We find that the presence of defect sources relaxes the constraints on globally well-defined T-brane configurations, avoiding the obstruction to building them on surfaces of positive curvature. Profiles with poles can be understood, from a 4d viewpoint, as non-trivial vevs for massive modes induced by the defects, and come with their own set of constraints. In the special case of fields localised on a self-intersection curve, we show how to retrieve the Hitchin system with defects from an ordinary global one with enhanced symmetry., 44 pages + appendices

We use the F-theoretic engineering of four-dimensional rank-one superconformal field theories to provide a geometric understanding of the phenomenon of supersymmetry enhancement along the RG flow, recently observed by Maruyoshi and Song. In this context, the superpotential deformations responsible for such flows are interpreted as T-brane backgrounds and encoded in the geometry of elliptically-fibered fourfolds. We formulate a simple algebraic criterion to select all supersymmetry-enhancing flows and, without any maximization process, derive the main features of the corresponding N=2 theories in the infrared., 19 pages + 1 appendix, 1 figure

We analyse global aspects of 7-brane backgrounds with a non-commuting profile for their worldvolume scalars, also known as T-branes. In particular, we consider configurations with no poles and globally well-defined over a compact K\"ahler surface. We find that such T-branes cannot be constructed on surfaces of positive or vanishing Ricci curvature. For the existing T-branes, we discuss their stability as we move in K\"ahler moduli space at large volume and provide examples of T-branes splitting into non-mutually-supersymmetric constituents as they cross a stability wall., Comment: 37 pages, 1 figure, 2 appendices; minor corrections and reference added

We examine SL(2, Z) anomalies in ten and eight-dimensional supergravities, the induced local counterterms and their realization in string theory. Composite connections play an important role in the cancellation mechanism. At the same time their global properties lead to novel non-trivial consistency constraints on compactifications., Comment: 29 pages; Minor changes and clarifications. Version to apper in JHEP

We consider N = 1 F-theory and Type IIB orientifold compactifications and derive new α ′ corrections to the four-dimensional effective action. They originate from higher derivative corrections to eleven-dimensional supergravity and survive the M-theory to F-theory limit. We find a correction to the Kahler potential depending on the volume of a non-trivial intersection curve of seven-branes. At weak string coupling this correction arises from the intersection of D7-branes with the O7-plane. We also analyze a four-dimensional higher curvature correction.

T-branes are exotic bound states of D-branes, characterized by mutually non-commuting vacuum expectation values for the worldvolume scalars. The M/F-theory geometry lifting D6/D7-brane configurations is blind to the T-brane data. In this paper, we make this data manifest, by probing the geometry with an M2-brane. We find that the effect of a T-brane is to deform the membrane worldvolume superpotential with monopole operators, which partially break the three-dimensional flavor symmetry, and reduce super-symmetry from N = 4 to N = 2. Our main tool is 3d mirror symmetry. Through this language, a very concrete framework is developed for understanding T-branes in M-theory. This leads us to uncover a new class of N = 2 quiver gauge theories, whose Higgs branches mimic those of membranes at ADE singularities, but whose Coulomb branches differ from their N = 4 counterparts., SCOPUS: ar.j, info:eu-repo/semantics/published

Bound states of 7-branes known as ‘T-branes’ have properties that defy usual geometric intuition. For instance, the gauge group of n coincident branes may not be U(n). More surprisingly, matter may show up at unexpected loci, such as points. By analyzing T-branes of perturbative type IIB string theory in the tachyon condensation picture we gain the following insights: in a large class of models, the tachyon can be diagonalized even though the worldvolume Higgs cannot. In those cases, we see the structure of these bound states more manifestly, thereby drastically simplifying analysis of gauge groups and spectra. Whenever the tachyon is not diagonalizable, matter localizes at unexpected loci, and we find that there is a lower-dimensional brane bound to the 7-brane., SCOPUS: ar.j, info:eu-repo/semantics/published

We propose a framework for treating F-theory directly, without resolving or deforming its singularities. This allows us to explore new sectors of gauge theories, including exotic bound states such as T-branes, in a global context. We use the mathematical framework known as Eisenbud’s matrix factorizations for hypersurface singularities. We display the usefulness of this technique by way of examples, including affine singularities of both conifold and orbifold type, as well as a class of full-fledged compact elliptically fibered Calabi-Yau fourfolds., SCOPUS: ar.j, info:eu-repo/semantics/published

We consider the weak coupling limit of F-theory in the presence of non-Abelian gauge groups implemented using the traditional ansatz coming from Tate's algorithm. We classify the types of singularities that could appear in the weak coupling limit and explain their resolution. In particular, the weak coupling limit of SU(n) gauge groups leads to an orientifold theory which suffers from conifold singulaties that do not admit a crepant resolution compatible with the orientifold involution. We present a simple resolution to this problem by introducing a new weak coupling regime that admits singularities compatible with both a crepant resolution and an orientifold symmetry. We also comment on possible applications of the new limit to model building. We finally discuss other unexpected phenomena as for example the existence of several non-equivalent directions to flow from strong to weak coupling leading to different gauge groups., 34 pages

We study the quantization of the M-theory G-flux on elliptically fibered Calabi-Yau fourfolds with singularities giving rise to unitary and symplectic gauge groups. We seek and find its relation to the Freed-Witten quantization of worldvolume uxes on 7-branes in type IIB orientifold compactifications on Calabi-Yau threefolds. By explicitly constructing the appropriate four-cycles on which to calculate the periods of the second Chern class of the fourfolds, we find that there is a half-integral shift in the quantization of G-flux whenever the corresponding dual 7-brane is wrapped on a non-spin submanifold. This correspondence of quantizations holds for all unitary and symplectic gauge groups, except for SU(3), which behaves mysteriously. We also perform our analysis in the case where, in addition to the aforementioned gauge groups, there is also a flavor' U(1)-gauge group., SCOPUS: ar.j, info:eu-repo/semantics/published

We consider the two main classification methods of D-brane charges via K-theory, in type II superstring theory with vanishing B-field: the Gysin map approach and the one based on the Atiyah-Hirzebruch spectral sequence. Then, we find out an explicit link between these two approaches: the Gysin map provides a representative element of the equivalence class obtained via the spectral sequence. We also briefly discuss the case of rational coefficients, characterized by a complete equivalence between the two classification methods., Comment: 34 pages, no figures

We compactify four-dimensional N=1 gauged supergravity theories on a circle including fluxes for shift-symmetric scalars. Four-dimensional Taub-NUT gravitational instantons universally correct the three-dimensional superpotential in the absence of fluxes. In the presence of fluxes these Taub-NUT instanton contributions are no longer gauge-invariant. Invariance can be restored by gauge instantons on top of Taub-NUT instantons. We establish the embedding of this scenario into M-theory. Circle fluxes and gaugings arise from a restricted class of M-theory four-form fluxes on a resolved Calabi-Yau fourfold. The M5-brane on the base of the elliptic fourfold dualizes into the universal Taub-NUT instanton. In the presence of fluxes this M5-brane is anomalous. We argue that anomaly free contributions arise from involved M5-brane geometries dual to gauge-instantons on top of Taub-NUT instantons. Adding a four-dimensional superpotential to the gravitational instanton corrections leads to three-dimensional Anti-de Sitter vacua at stabilized compactification radius. We comment on the possibility to uplift these M-theory vacua, and to tunnel to four-dimensional F-theory vacua., Comment: 47 pages, 2 figures

We study the problem of four-form flux quantization in F-theory compactifications. We prove that for smooth, elliptically fibered Calabi-Yau fourfolds with a Weierstrass representation, the flux is always integrally quantized. This implies that any possible half-integral quantization effects must come from 7-branes, i.e. from singularities of the fourfold. We subsequently analyze the quantization rule on explicit fourfolds with Sp(N) singularities, and connect our findings via Sen's limit to IIB string theory. Via direct computations we find that the four-form is half-integrally quantized whenever the corresponding 7-brane stacks wrap non-spin complex surfaces, in accordance with the perturbative Freed-Witten anomaly. Our calculations on the fourfolds are done via toric techniques, whereas in IIB we rely on Sen's tachyon condensation picture to treat bound states of branes. Finally, we give general formulae for the curvature- and flux-induced D3 tadpoles for general fourfolds with Sp(N) singularities., 46 pages

In order to describe the appearance in F theory of the non--simply--laced Lie algebras, we use the representation of symmetry enhancements by means of string junctions. After an introduction to the techniques used to describe symmetry enhancement, that is algebraic geometry, BPS states analysis and string junctions, we concentrate on the latter. We give an explicit description of the folding of D_{2n} to B_n of the folding of E_6 to F_4 and that of D_4 to G_2 in terms of junctions and Jordan strings. We also discuss the case of C_n, but we are unable in this case to provide a string interpretation., 24 pages, 3 figures

We study the effective physics of F-theory at order α ′ 3 in derivative expansion. We show that the ten-dimensional type IIB eight-derivative couplings involving the graviton and the axio-dilaton naturally descend from pure gravity in twelve dimensions. Upon compactification on elliptically fibered Calabi-Yau fourfolds, the non-trivial vacuum profile for the axio-dilaton leads to a new, genuinely N = 1 , α ′ 3 $$ \mathcal{N} = 1,\ {\alpha}^{\prime\ 3} $$ correction to the four-dimensional effective action.

T-branes are supersymmetric configurations described by multiple Dp-branes with worldvolume flux and non-commuting vacuum expectation values for two of the worldvolume scalars. When these values are much larger than the string scale this description breaks down. We show that in this regime the correct description of T-branes is in terms of a single Dp-brane, whose worldvolume curvature encodes the T-brane data. We present the tale of the journey to reach this picture, which takes us through T-dualities and rugby-ball-shaped brane configurations that no eye has gazed upon before., Comment: 19 pages, 4 figures

We "solve" the Freed-Witten anomaly equation, i.e., we find a geometrical classification of the B-field and A-field configurations in the presence of D-branes that are anomaly-free. The mathematical setting being provided by the geometry of gerbes, we find that the allowed configurations are jointly described by a coset of a certain hypercohomology group. We then describe in detail various cases that arise according to such classification. As is well-known, only under suitable hypotheses the A-field turns out to be a connection on a canonical gauge bundle. However, even in these cases, there is a residual freedom in the choice of the bundle, naturally arising from the hypercohomological description. For a B-field which is flat on a D-brane, fractional or irrational charges of subbranes naturally appear; for a suitable gauge choice, they can be seen as arising from "gauge bundles with not integral Chern class": we give a precise geometric interpretation of these objects., Comment: 28 pages, no figures

We study the relations between pin structures on a non-orientable even-dimensional manifold, with or without boundary, and pin structures on its orientable double cover, requiring the latter to be invariant under sheet-exchange. We show that there is not a simple bijection, but that the natural map induced by pull-back is neither injective nor surjective: we thus find the conditions to recover a full correspondence. We also show how to describe such a correspondence using spinors instead of pinors on the double cover: this is in a certain sense possible, but in a way that contains anyhow an explicit reference to pinors. We then consider the example of surfaces, with detailed computations for the real projective plane, the Klein bottle and the Moebius strip., Comment: 28 pages, no figures