Search

In order to be in control of the $\alpha'$ derivative expansion, geometric string compactifications are understood in the context of a large volume approximation. In this letter, we consider the reduction of these higher derivative terms, and propose an improved estimate on the large volume approximation using numerical Calabi-Yau metrics obtained via machine learning methods. Further to this, we consider the $\alpha'^3$ corrections to numerical Calabi-Yau metrics in the context of IIB string theory. This correction represents one of several important contributions for realistic string compactifications -- alongside, for example, the backreaction of fluxes and local sources -- all of which have important consequences for string phenomenology. As a simple application of the corrected metric, we compute the change to the spectrum of the scalar Laplacian.

In this work, we develop a tool to study string perturbation theory of the Klebanov-Strassler solution in the large radius approximation based on open-closed superstring field theory. Combining the large radius expansion and a double scaling limit, we find a perturbative background solution of open-closed superstring field theory that corresponds to the Klebanov-Strassler solution. To illustrate the utilities of this approach, we break supersymmetry of the background by placing a stack of anti-D3-branes at the tip of the throat. We then find a perturbative open string background solution to the third order in the large radius approximation, which agrees with the well-known supergravity analysis of Kachru-Pearson-Verlinde (KPV) on the stability of the antiD3-brane supersymmetry breaking. The perturbative background solution to the open string field theory we found is expected to be dual to an NS5-brane probing the KS solution., Comment: minor errors corrected, results unchanged, 96 pages

We demonstrate how recent developments in string field theory provide a framework to systematically study type II flux compactifications with non-trivial Ramond-Ramond profiles. We present an explicit example where physical observables can be computed order by order in a small parameter which can be effectively viewed as string coupling constant. We obtain the corresponding background solution of the string field equations of motions up to the second order in the expansion. Along the way, we show how the tadpole cancellations of the string field equations lead to the minimization of the F-term potential of the low energy supergravity description. String field action expanded around the obtained background solution furnishes a worldsheet description of the flux compactifications., Comment: v2: discussion on massless tadpole and string field equations corrected, string field solution fixed accordingly

This manuscript concerns string one-loop corrections to the Kahler potential in 4d N=1 vacua of string theories, and it largely consists of two parts. In the first part, we compute the string one-loop correction to the dilaton kinetic term in heterotic string theories, and we show that the dilaton kinetic term is not renormalized at one-loop. After reviewing the well-known result on the string one-loop correction to the Kahler potential in heterotic string theories, we explain how this result can be reconciled with the known result in the literature. In the second part, we study the dilaton dependence of the one-loop corrected Kahler potential in type II string theories. To do so, we compute the string one-loop correction to the kinetic action of the 4d-dilaton in type II string theories compactified on orientifolds of Calabi-Yau threefolds. We find that the string one-loop corrected 4d dilaton kinetic term is determined by the Witten index and the new supersymmetric index of the string worldsheet CFT., Comment: v2: 59 pages. It was found that even at the four fermi level, vertex collisions can generate an enhancement by the factor of 1/delta. Such corrections are correctly included in the computation. v3: typos fixed. v4: Typos fixed, discussions expanded

We present an efficient algorithm for computing the prepotential in compactifications of type II string theory on mirror pairs of Calabi-Yau threefolds in toric varieties. Applying this method, we exhibit the first systematic computation of genus-zero Gopakumar-Vafa invariants in compact threefolds with many moduli, including examples with up to 491 vector multiplets., Comment: v1: 44 pages, 4 figures; v2: matches published version

To compute the string one-loop correction to the Kahler potential of moduli fields of string compactifications in Einstein-frame, one must compute: the string one-loop correction to the Einstein-Hilbert action, the string one-loop correction to the moduli kinetic terms, the string one-loop correction to the definition of the holomorphic coordinates. In this note, we compute the string one-loop correction to the Einstein-Hilbert action of type II string theory compactified on orientifolds of Calabi-Yau threefolds. We find that the one-loop correction is determined by the new supersymmetric index studied by Cecotti, Fendley, Intriligator, and Vafa. As a simple application, we apply our results to estimate the size of the one-loop corrections around a conifold point in the Kahler moduli space., Comment: v2: minor errors fixed. v3: additional check provided by comparing to the known R^4 term. v5: normalization of PCO fixed. v6: matches JHEP version. Discussions expanded. v7: minor errors fixed

In this note, we prove that the one-loop pfaffian of the non-perturbative superpotential generated by Euclidean D-branes in type II compactifications on orientifolds of Calabi-Yau threefolds is determined by the moduli integral of the new supersymmetric index defined by Cecotti, Fendley, Intriligator, and Vafa. As this quantity can be computed via topological string theory, Chern-Simons theory, matrix models, or by solving the holomorphic anomaly equation, this result provides a method to directly compute the one-loop pfaffian of the non-perturbative superpotential. The relation between the one-loop pfaffian, threshold corrections to the gauge coupling, and the one-loop partition function of open topological string theory is discussed., Comment: v2: 17 pages. Typos fixed. References added. Some discussions expanded. v3: 18 pages. References added. v4: matches jhep version

We study Euclidean M5-branes wrapping vertical divisors in elliptic Calabi-Yau fourfold compactifications of M/F-theory that admit a Sen limit. We construct these Calabi-Yau fourfolds as elliptic fibrations over coordinate flip O3/O7 orientifolds of toric hypersurface Calabi-Yau threefolds. We devise a method to analyze the Hodge structure (and hence the dimension of the intermediate Jacobian) of vertical divisors in these fourfolds, using only the data available from a type IIB compactification on the O3/O7 Calabi-Yau orientifold. Our method utilizes simple combinatorial formulae (that we prove) for the equivariant Hodge numbers of the Calabi-Yau orientifolds and their prime toric divisors, along with a formula for the Euler characteristic of vertical divisors in the corresponding elliptic Calabi-Yau fourfold. Our formula for the Euler characteristic includes a conjectured correction term that accounts for the contributions of pointlike terminal $\mathbb{Z}_2$ singularities corresponding to perturbative O3-planes. We check our conjecture in a number of explicit examples and find perfect agreement with the results of direct computations., Comment: 110 pages plus appendices. Reviews various aspects of toric geometry, including toric hypersurfaces and stratifications. v2: Corrected minor typos, clarifications about vacua to which our results apply. v3: Corrected typos in appendix, added comment and reference regarding Picard rank of an Enriques surface in Section 6.3. v4: Added a reference for algorithm for identifying orientifold fixed loci

We study the D3-brane moduli dependence of the non-perturbative superpotential generated by the D7-brane gaugino condensation in a type IIB compactification on an orientifold of the elliptic Calabi-Yau threefold $\Bbb{P}_{[1,1,1,6,9]}[18].$ Building on the work of Ganor, in the weak coupling limit, we compute the D3-brane dependent one-loop pfaffian in the flat coordinates and find that the one-loop pfaffian is written as the Jacobi theta function. We also comment on the complex structure dependence of the D3-brane dependent one-loop pfaffian., Comment: 16 pages

We study Euclidean D3-branes wrapping divisors $D$ in Calabi-Yau orientifold compactifications of type IIB string theory. Witten's counting of fermion zero modes in terms of the cohomology of the structure sheaf $\mathcal{O}_D$ applies when $D$ is smooth, but we argue that effective divisors of Calabi-Yau threefolds typically have singularities along rational curves. We generalize the counting of fermion zero modes to such singular divisors, in terms of the cohomology of the structure sheaf $\mathcal{O}_{\overline{D}}$ of the normalization $\overline{D}$ of $D$. We establish this by detailing compactifications in which the singularities can be unwound by passing through flop transitions, giving a physical incarnation of the normalization process. Analytically continuing the superpotential through the flops, we find that singular divisors whose normalizations are rigid can contribute to the superpotential: specifically, $h^{\bullet}_{+}(\mathcal{O}_{\overline{D}})=(1,0,0)$ and $h^{\bullet}_{-}(\mathcal{O}_{\overline{D}})=(0,0,0)$ give a sufficient condition for a contribution. The examples that we present feature infinitely many isomorphic geometric phases, with corresponding infinite-order monodromy groups $\Gamma$. We use the action of $\Gamma$ on effective divisors to determine the exact effective cones, which have infinitely many generators. The resulting nonperturbative superpotentials are Jacobi theta functions, whose modular symmetries suggest the existence of strong-weak coupling dualities involving inversion of divisor volumes., Comment: 31 pages, 4 figures

We use string field theory to fix the normalization of the D-instanton corrections to the superpotential involving the moduli fields of type II string theory compactified on an orientifold of a Calabi-Yau threefold in the absence of fluxes. We focus on $O(1)$ instantons whose only zero modes are the four bosonic modes associated with translation of the instanton in non-compact directions and a pair of fermionic zero modes associated with the two supercharges broken by the instanton. We work with a generic superconformal field theory and express our answer in terms of the spectrum of open strings on the instanton. We analyse the contribution of multi-instantons of this kind to the superpotential and argue that it vanishes when background fluxes are absent., Comment: 34+31 pages; v2: references added

We study the non-perturbative superpotential generated by D(-1)-branes in type IIB compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. To compute the D-instanton superpotential, we study F-theory compactification on toric complete intersection elliptic Calabi-Yau fourfolds. We take the Sen-limit, but with finite $g_s,$ in F-theory compactification with a restriction that all D7-branes are carrying SO(8) gauge groups, which we call the global Sen-limit. In the global Sen-limit, the axio-dilaton is not varying in the compactification manifold. We compute the Picard-Fuchs equations of elliptic Calabi-Yau fourfolds in the global Sen-limit, and show that the Picard-Fuchs equations of the elliptic fourfolds split into that of the underlying Calabi-Yau threefolds and of the elliptic fiber. We then demonstrate that this splitting property of the Picard-Fuchs equation implies that the fourform period of the elliptic Calabi-Yau fourfolds in the global Sen-limit does not contain exponentially suppressed terms $\mathcal{O}(e^{-\pi/g_s})$. With this result, we finally show that in the global Sen-limit, the superpotential of the underlying type IIB compactification does not receive D(-1)-instanton contributions. This result is exact in $g_s.$, Comment: v5. 36 pages. Clarifications added. Results unchanged

In this note, we prove combinatorial formulas for $h^{2,1}$ of prime toric divisors in an arbitrary toric hypersurface Calabi-Yau fourfold $Y_4.$ We show that it is possible to find a toric hypersurface Calabi-Yau in which there are more than $h^{1,1}(Y_4)$ non-perturbative superpotential terms with trivial intermediate Jacobian. Hodge numbers of divisors in toric CICYs are the subjects of the part two., Comment: v2. References added

We construct a vacuum of string theory in which the magnitude of the vacuum energy is $< 10^{-123}$ in Planck units. Regrettably, the sign of the vacuum energy is negative, and some supersymmetry remains unbroken., Comment: 6 pages. A more detailed analysis appears in our companion paper 2107.09064. v2: typo fixed, results unchanged; approximately matches version published in PRL

We construct supersymmetric $\mathrm{AdS}_4$ vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the $\alpha'$ expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude $ < 10^{-123}$ in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol., Comment: 55 pages, 6 figures, one appendix. A summary of these results appears in the companion paper arXiv:2107.09065. Compactification data included in ancillary files. v2: typos fixed, references added. v3: extended discussion, typos fixed, results unchanged; matches version published in JHEP

This is the second in a two-part paper devoted to studying entanglement entropy and edge modes in the A model topological string theory. This theory enjoys a gauge-string (Gopakumar-Vafa) duality which is a topological analogue of AdS/CFT. In part 1, we defined a notion of generalized entropy for the topological closed string theory on the resolved conifold. We provided a canonical interpretation of the generalized entropy in terms of the q-deformed entanglement entropy of the Hartle-Hawking state. We found string edge modes transforming under a quantum group symmetry and interpreted them as entanglement branes. In this work, we provide the dual Chern-Simons gauge theory description. Using Gopakumar-Vafa duality, we map the closed string theory Hartle-Hawking state to a Chern-Simons theory state containing a superposition of Wilson loops. These Wilson loops are dual to closed string worldsheets that determine the partition function of the resolved conifold. We show that the undeformed entanglement entropy due to cutting these Wilson loops reproduces the bulk generalized entropy and therefore captures the entanglement underlying the bulk spacetime. Finally, we show that under the Gopakumar-Vafa duality, the bulk entanglement branes are mapped to a configuration of topological D-branes, and the non-local entanglement boundary condition in the bulk is mapped to a local boundary condition in the gauge theory dual. This suggests that the geometric transition underlying the gauge-string duality may also be responsible for the emergence of entanglement branes., Comment: typos corrected, updated the conclusion and discussion of the defect operator in section 2.5, one new figure, and references added

Progress in identifying the bulk microstate interpretation of the Ryu-Takayanagi formula requires understanding how to define entanglement entropy in the bulk closed string theory. Unfortunately, entanglement and Hilbert space factorization remains poorly understood in string theory. As a toy model for AdS/CFT, we study the entanglement entropy of closed strings in the topological A-model in the context of Gopakumar-Vafa duality. We will present our results in two separate papers. In this work, we consider the bulk closed string theory on the resolved conifold and give a self-consistent factorization of the closed string Hilbert space using extended TQFT methods. We incorporate our factorization map into a Frobenius algebra describing the fusion and splitting of Calabi-Yau manifolds, and find string edge modes transforming under a $q$-deformed surface symmetry group. We define a string theory analogue of the Hartle-Hawking state and give a canonical calculation of its entanglement entropy from the reduced density matrix. Our result matches with the geometrical replica trick calculation on the resolved conifold, as well as a dual Chern-Simons theory calculation which will appear in our next paper \cite{secondpaper}. We find a realization of the Susskind-Uglum proposal identifying the entanglement entropy of closed strings with the thermal entropy of open strings ending on entanglement branes. We also comment on the BPS microstate counting of the entanglement entropy. Finally we relate the nonlocal aspects of our factorization map to analogous phenomenon recently found in JT gravity., Comment: Typos corrected and citations added

We introduce a method for finding flux vacua of type IIB string theory in which the flux superpotential is exponentially small and at the same time one or more complex structure moduli are stabilized exponentially near to conifold points., Comment: 44 pages, 5 figures. v2: extended discussion of near-conifold expansion of prepotential, references added

We describe a method for finding flux vacua of type IIB string theory in which the Gukov-Vafa-Witten superpotential is exponentially small. We present an example with $W_0 \approx 2 \times 10^{-8}$ on an orientifold of a Calabi-Yau hypersurface with $(h^{1,1},h^{2,1})=(2,272)$, at large complex structure and weak string coupling., Comment: 5 pages, 1 figure. v2: refs added, minor corrections, results unchanged

We analyze the de Sitter construction of \cite{KKLT} using ten-dimensional supergravity, finding exact agreement with the four-dimensional effective theory. Starting from the fermionic couplings in the D7-brane action, we derive the ten-dimensional stress-energy due to gaugino condensation on D7-branes. We demonstrate that upon including this stress-energy, as well as that due to anti-D3-branes, the ten-dimensional equations of motion require the four-dimensional curvature to take precisely the value determined by the four-dimensional effective theory of \cite{KKLT}., Comment: 58 pages. v2: corrected statements about generalized complex geometry. Appendices contain more details of spinor ansatz and of D3-brane potential. Typos fixed, refs added. v3: significant additional results. Appendix A includes analysis of a new term in the Killing spinor equations. Appendix C contains a demonstration of the cancellation of divergences. Conclusions unchanged

In axion monodromy inflation, traversing $N$ axion periods corresponds to discharging $N$ units of a quantized charge. In certain models with moving D7-branes, such as Higgs-otic inflation, this monodromy charge is D3-brane charge induced on the D7-branes. The stress-energy of the induced charge affects the internal space, changing the inflaton potential and potentially limiting the field range. We compute the backreaction of induced D3-brane charge in Higgs-otic inflation. The effect on the nonperturbative superpotential is dramatic even for $N=1$, and may preclude large-field inflation in this model in the absence of a mechanism to control the backreaction., Comment: 31 pages

We study under which conditions a scalar particle is a viable WIMP Dark Matter candidate with Higgs and dilaton interactions. The theory is a composite Higgs model with top partial compositeness where both the Higgs and the Dark Matter candidate arise as pseudo Goldstone boson of the coset SO(6)/SO(5) from a new physics sector. We highlight the role of the dilaton in direct and indirect searches. We find that a Dark Matter particle with a mass around 200-400 GeV and a relatively light dilaton are a fair prediction of the model., Comment: 16 pages