We study 5-dimensional supergravity on S^1/Z_2 with a physical Z_2-odd vector multiplet, which yields an additional modulus other than the radion. We derive 4-dimensional effective theory and find additional terms in the Kahler potential that are peculiar to the multi moduli case. Such terms can avoid tachyonic soft scalar masses at tree-level, which are problematic in the single modulus case. We also show that the flavor structure of the soft terms are different from that in the single modulus case when hierarchical Yukawa couplings are generated by wavefunction localization in the fifth dimension. We present a concrete model that stabilizes the moduli at a supersymmetry breaking Minkowski minimum, and show the low energy sparticle spectrum.
5D supergravity generically has non-geometric moduli other than the radion that belong to 5D vector multiplets. We summarize the impacts of such moduli on 4D effective theory of 5D supergravity on S^1/Z_2. We mainly discuss the structure of the effective Kahler potential including the one-loop quantum corrections. As an illustrative example, we construct a model in which the size of the extra dimension is stabilized at an exponentially large value compared to the Planck length, which is similar to the LARGE volume scenario in string theory.
We revisit the issue of moduli stabilization in a class of N=1 four dimensional supergravity theories which are low energy descriptions of standard perturbative heterotic string vacua compactified on Calabi-Yau spaces. In particular, we show how it is possible to stabilize the universal dilaton and Kahler moduli in a de Sitter/Minkowski vacuum with low energy supersymmetry breaking by means of non-perturbative gauge dynamics, including recent results by Intriligator, Seiberg and Shih. The non-SUSY vacua are meta-stable but sufficiently long-lived.
We perform a comprehensive and systematic analysis of the SUSY flavor structure of generic 5D supergravity models on $S^1/Z_2$ with multiple $Z_2$-odd vector multiplets that generate multiple moduli. The SUSY flavor problem can be avoided due to contact terms in the 4D effective Kähler potential peculiar to the multi-moduli case. A detailed phenomenological analysis is provided based on an illustrative model.
We express the action of six-dimensional supergravity in terms of four-dimensional N=1 superfields, focusing on the moduli dependence of the action. The gauge invariance of the action in the tensor-vector sector is realized in a quite nontrivial manner, and it determines the moduli dependence of the action. The resultant moduli dependence is intricate, especially on the shape modulus. Our result is reduced to the known superfield actions of six-dimensional global SUSY theories and of five-dimensional supergravity by replacing the moduli superfields with their background values and by performin…
We study a four-dimensional effective theory of the five-dimensional (5D) gauged supergravity with a universal hypermultiplet and perturbative superpotential terms at the orbifold fixed points. Among eight independent isometries of the scalar manifold, we focus on three directions for gauging by the graviphoton. The class of models we consider includes the 5D heterotic M-theory and the supersymmetric Randall-Sundrum model as special limits of the gauging parameters. We analyze the vacuum structure of such models, especially the nature of moduli stabilization, from the viewpoint of the effectiv…
We study domain wall solutions in d=5, N=2 supergravity coupled to a single hypermultiplet whose moduli space is described by certain inhomogeneous, toric ESD manifolds constructed recently by Calderbank and Singer. Upon gauging a generic U(1) isometry of these spaces, we obtain an infinite family of models whose "superpotential" admits an arbitrary number of isolated critical points. By investigating the associated supersymmetric flows, we prove the existence of domain walls of Randall-Sundrum type for each member of our family, and find chains of domain walls interpolating between various Ad…
We construct a natural inflation model in supergravity where the inflaton is identified with a modulus field possessing a shift symmetry. The superpotential for the inflaton is generated by meson condensation due to strong dynamics with deformed moduli constraints. In contrast to models based on gaugino condensation, the inflaton potential is generated without $R$-symmetry breaking and hence does not depend on the gravitino mass. Thus, our model is compatible with low scale supersymmetry.
We study the structure of the supersymmetric moduli spaces of ${\cal N}=1$ and ${\cal N}=2$ supergravity theories in $AdS_4$ backgrounds. In the ${\cal N}=1$ case, the moduli space cannot be a complex submanifold of the Kähler field space, but is instead real with respect to the inherited complex structure. In ${\cal N}=2$ supergravity the same result holds for the vector multiplet moduli space, while the hypermultiplet moduli space is a Kähler submanifold of the quaternionic-Kähler field space. These findings are in agreement with AdS/CFT considerations.
We propose a simple but effective mechanism to realize an inflationary early universe consistent with the observed WMAP, Planck and/or BICEP2 data, which would be incorporated in various supersymmetric models of elementary particles constructed in the (effective) five-dimensional spacetime. In our scenario, the inflaton field is identified with one of the moduli appearing when the fifth direction is compactified, and a successful cosmological inflation without the so-called eta problem can be achieved by a very simple moduli stabilization potential. We also discuss the related particle cosmolo…
We show that the conifold and deformed-conifold warped compactifications of the ten-dimensional type IIB supergravity, including the Klebanov-Strassler solution, are dynamically unstable in the moduli sector representing the scale of a Calabi-Yau space, although it can be practically stable for a quite long time in a region with a large warp factor. This instability is associated with complete supersymmetry breaking except for a special case and produces significant time-dependence in the structure of the four-dimensional base spacetime as well as of the internal space.
This is an account of lectures that were given at TASI 2005, the Shanghai Summer School in M-theory 2005 and the Perimeter Institute. I review 1) the derivation of the potential for chiral scalar fields in ${\cal N}$=1 supergravity 2) the relation between F and D terms for chiral scalars, Weyl anomalies and the generation of non-perturbative terms in the superpotential and 3) the derivation of effective potentials for light moduli in type IIB string theory.
We construct the supergravity solution for fully localized D2/D6 intersection. The near horizon limit of this solution is the supergravity dual of supersymmetric Yang-Mills theory in 2+1 dimensions with flavor. We use this solution to formulate mirror symmetry of 2+1 dimensional gauge theories in the language of AdS/CFT correspondence. We also construct the supergravity dual of a non-commutative gauge theory with fundamental matter.
We calculate the scalar potential of supersymmetric QCD (in the regime N_f < N_c) coupled to N=1 supergravity with moduli-dependent gauge kinetic function and masses. The gauge dynamics are described by the Taylor-Veneziano-Yankielowicz superpotential for composite effective fields. The potential can be expanded about the ``truncated'' point in the gaugino and matter condensate directions in order to find corrections to the globally supersymmetric minimum. The results are relevant to the phenomenology of supersymmetry-breaking in string-inspired supergravity models, and also to recent work on …
In this talk we review some results concerning a mechanism for reducing the moduli space of a topological field theory to a proper submanifold of the ordinary moduli space. Such mechanism is explicitly realized in the example of constrained topological gravity, obtained by topologically twisting the N=2 Liouville theory.
We investigate 5-dimensional supergravity on S^1/Z_2 with a physical Z_2-odd vector multiplet, which yields an additional modulus other than the radion. We find additional terms in the 4-dimensional effective theory that are peculiar to the multi moduli case. Such terms can make the soft masses are non-tachyonic and almost flavor-universal at tree-level, in contrast to the single modulus case. This provides a new possibility to solve the SUSY flavor problem.
The simple chaotic inflation is highly consistent with the BICEP2 experiment, and no-scale supergravity can be realized naturally in various string compactifications. Thus, we construct a chaotic inflation model in no-scale supergravity inspired from Type IIB string compactification with an anomalous U(1)_X gauged symmetry. We introduce two moduli T_1 and T_2 which transform non-trivially under U(1)_X, and some pairs of fundamental quarks charged under the SU(N) x U(1)_X gauge group. The non-trivial transformations of moduli under U(1)_X lead to a moduli-dependent Fayet-Iliopoulos (FI) term. T…
We determine the conditions for maximally supersymmetric AdS_5 vacua of five-dimensional gauged N=2 supergravity coupled to vector-, tensor- and hypermultiplets charged under an arbitrary gauge group. In particular, we show that the unbroken gauge group of the AdS_5 vacua has to contain an U(1)_R-factor. Moreover we prove that the scalar deformations which preserve all supercharges form a Kahler submanifold of the ambient quaternionic Kahler manifold spanned by the scalars in the hypermultiplets.
We consider the conditions for integrating out heavy chiral fields and moduli in N=1 supergravity, subject to two explicit requirements. First, the expectation values of the heavy fields should be unaffected by low energy phenomena. Second, the low energy effective action should be described by N=1 supergravity. This leads to a working definition of decoupling in N=1 supergravity that is different from the usual condition of gravitational strength couplings between sectors, and that is the relevant one for inflation with moduli stabilization, where some light fields (the inflaton) can have lon…
Anti-D3 branes and non-perturbative effects in flux compactifications spontaneously break supersymmetry and stabilise moduli in a metastable de Sitter vacua. The low energy 4D effective field theory description for such models would be a supergravity theory with non-linearly realised supersymmetry. Guided by string theory modular symmetry, we compute this non-linear supergravity theory, including dependence on all bulk moduli. Using either a constrained chiral superfield or a constrained vector field, the uplifting contribution to the scalar potential from the anti-D3 brane can be parameterise…
In certain class of flux compactification, moduli mediated supersymmetry (SUSY) breaking preserves flavor and CP at leading order in the perturbative expansion controlled by the vacuum expectation value of the messenger modulus. Nevertheless there still might be dangerous flavor or CP violation induced by higher order Kähler potential. We examine the constraints on such SUSY breaking scheme imposed by low energy flavor and/or CP violating observables. It is found that all phenomenological constraints can be satisfied even for generic form of higher order Kähler potential and sparticle spectra …
We analyze the moduli space of spontaneously broken N=8 supergravity theories in 4 dimensions with classical Minkowski vacua. We find that all the known classical vacua, as well as the several new ones we construct here, can be connected by sending some of the moduli to their boundary values. We also show that Cremmer-Scherk-Schwarz models can be viewed as special limits of more general CSO* gaugings, which allow for non-Abelian residual symmetries on the vacuum. Finally, we find that all the classical Minkowski vacua with fully broken supersymmetry found so far are unstable with respect to 1-…
We present a twistor-like formula for the complete tree-level S matrix of 6D $(2,0)$ supergravity coupled to $21$ abelian tensor multiplets. This is the low-energy effective theory that corresponds to Type IIB superstring theory compactified on a $\mathrm{K}3$ surface. The formula is expressed as an integral over the moduli space of certain rational maps of the punctured Riemann sphere. By studying soft limits of the formula, we are able to explore the local moduli space of this theory, ${SO(5,21)\over SO(5)\times SO(21)}$. Finally, by dimensional reduction, we also obtain a new formula for th…
The untwisted moduli in four-dimensional fermionic string models are identified by considering world-sheet Abelian Thirring interactions. The full Kahler potentials of untwisted sector fields are given for a restricted class of models.
We obtain the supergravity dual of N=1 supersymmetric gauge theory in 2+1 dimensions with a large number of unquenched massless flavors. The geometries found are obtained by solving the equations of motion of supergravity coupled to a suitable continuous distribution of flavor branes. The background obtained preserves two supersymmetries. We find that when N_c\ge 2N_f the behavior of the solutions is compatible with having an asymptotically free dual gauge theory with dynamical quarks. On the contrary, when N_c<2N_f the theory develops a Landau pole in the UV. We also find a new family of (unf…
We study the moduli stabilization from the viewpoint of modular flavor symmetries. We systematically analyze stabilized moduli values in possible configurations of flux compactifications, investigating probabilities of moduli values and showing which moduli values are favorable from our moduli stabilization. Then, we examine their implications on modular symmetric flavor models. It is found that distributions of complex structure modulus $τ$ determining the flavor structure are clustered at a fixed point with the residual $\mathbb{Z}_3$ symmetry in the $SL(2,\mathbb{Z})$ fundamental region. Al…
We construct an explicit 5-dimensional supergravity model that realizes the "no scale" mechanism for supersymmetry breaking with no unstable moduli. Supersymmetry is broken by a constant superpotential localized on a brane, and the radion is stabilized by Casimir energy from supergravity and massive hypermultiplets. If the standard model gauge and matter fields are localized on a brane, then visible sector supersymmetry breaking is dominated by gravity loops and flavor-violating hypermultiplet loops, and gaugino masses are smaller than scalar masses. We present a realistic model in which the t…
It is generally believed that weak scale supersymmetry implies weak scale supergravity, in the sense that the masses of the gravitino and gravitationally coupled moduli have masses below 100 TeV. This paper presents a realistic framework for supersymmetry breaking in the hidden sector in which the masses of the gravitino and gravitational moduli can be much larger. This cleanly eliminates the cosmological problems of hidden sector models. Supersymmetry breaking is communicated to the visible sector by anomaly-mediated supersymmetry breaking. The framework is compatible with perturbative gauge …
We study the glueballs in a four-dimensional ${\cal N}=2$ super Yang-Mills theory with fundamental matters in terms of the supergravity dual. The supergravity background is constructed by $N$ D3 brane with a probe D7 brane. We numerically compute the glueball masses for $0^{++}$ and $1^{--}$ in the background. We find that the mass ratio of $0^{++}$ glueballs is mostly in agreement with the lattice calculations. We compare the glueball masses with the meson masses. The mass ratio $M_{GB}/M_{meson}$ is calculated with 1.4. If the mass $M_{GB}$ is set to $1.6 GeV$, the meson mass $M_{meson}$ is …
We discuss a high-scale SUSY breaking scenario with the wino dark matter in the five-dimensional supergravity model on $S^1/Z_2$. The extra U(1) symmetries broken by the orbifold projection control the flavor structure of soft SUSY-breaking parameters as well as the Yukawa couplings, and a scalar component of the one of moduli multiplets, which arise from extra-dimensional components of the U(1) vector multiplets, induces the slow-roll inflation. Because of the supersymmetric moduli stabilization as well as the moduli inflation, it is found that the correct dark matter relic abundance is non-t…
We consider the D^6 R^4 term which is the leading contribution in the low momentum expansion of the three loop, four graviton amplitude in maximal supergravity. We calculate the moduli dependent coefficient of this term in 11 dimensional supergravity compactified on T^2. Only diagrams that involve the Mercedes skeleton contribute resulting in a compact expression involving an integral over 6 Schwinger parameters. We express this integral as an integral over the moduli of an auxiliary T^3. This includes an SL(3,Z) invariant integral over the shape moduli of the T^3. We discuss the renormalizati…
We consider gravity mediated supersymmetry (SUSY) breaking in 5D spacetime with two 4D branes B1 and B2 separated in the extra dimension. Using an off-shell 5D supergravity (SUGRA) formalism, we argue that the SUSY breaking scales could be non-universal even at the fundamental scale in a brane world setting, since SUSY breaking effects could be effectively localized. As an application, we suggest a model in which the two light chiral MSSM generations reside on B1, while the third generation is located on B2, and the Higgs multiplets as well as gravity and gauge multiplets reside in the bulk. F…
We study a symmetry breaking of residual flavor symmetries realized at fixed points of the moduli space. In the supersymmetric modular invariant theories, a small departure of the modulus from fixed points is required to realize fermion mass hierarchies and sizable CP-breaking effects. We investigate whether one can dynamically fix the moduli values in the vicinity of the fixed points in the context of Type IIB string theory. It is found that the string landscape prefers $|δτ| \simeq 10^{-5}$ for the deviation of the complex structure modulus from all fixed points and the CP-breaking vacuum is…
The role of moduli stabilization in predictions for CP violation is examined in the context of four-dimensional effective supergravity models obtained from the weakly coupled heterotic string. We point out that while stabilization of compactification moduli has been studied extensively, the determination of background values for other scalars by dynamical means has not been subjected to the same degree of scrutiny. These other complex scalars are important potential sources of CP violation and we show in a simple model how their background values (including complex phases) may be determined fr…
We consider models of inflation in supergravity with a shift symmetry. We focus on models with one moduli and one inflaton field. The presence of this symmetry guarantees the existence of a flat direction for the inflaton field. Mildly breaking the shift symmetry using a superpotential which depends not only on the moduli but also on the inflaton field allows one to lift the inflaton flat direction. Along the inflaton direction, the eta-problem is alleviated. Combining the KKLT mechanism for moduli stabilization and a shift symmetry breaking superpotential of the chaotic inflation type, we fin…
We consider gauged five dimensional supergravity with boundaries and vector multiplets in the bulk. We analyse the zero modes of the BPS configurations preserving N=1 supergravity at low energy. We find the 4d low energy effective action involving the moduli associated to the BPS zero modes. In particular, we derive the Kähler potential on the moduli space corresponding to the low energy 4d N=1 effective action.
We start with a particular cosmological model derived from type IIB supergravity theory with fluxes, where usually the dilaton is interpreted as a Quintessence field. Instead of that, in this letter we interpret the dilaton as the dark matter of the universe. With this alternative interpretation we find that in this supergravity model gives a similar evolution and structure formation of the universe compared with the $Λ$CDM model in the linear regime of fluctuations of the structure formation. Some free parameters of the theory are fixed using the present cosmological observations. In the non-…
We construct marginal operators of the orbifold SCFT corresponding to all twenty near-horizon moduli in supergravity, including operators involving twist fields which correspond to the blowing up modes. We identify the operators with the supergravity moduli in a 1-1 fashion by inventing a global SO(4) algebra in the SCFT. We analyze the gauge dynamics of the D1/D5 system relevant to the splitting $(Q_1,Q_5)\to (Q'_1,Q'_5)+ (Q''_1,Q''_5)$ with the help of a linear sigma model. We show in supergravity as well as in SCFT that the absorption cross-section for minimal scalars is the same all over t…
We review the ghost-free four-derivative terms for chiral superfields in $\mathcal{N}=1$ supersymmetry and supergravity. These terms induce cubic polynomial equations of motion for the chiral auxiliary fields and correct the scalar potential. We discuss the different solutions and argue that only one of them is consistent with the principles of effective field theory. Special attention is paid to the corrections along flat directions which can be stabilized or destabilized by the higher-derivative terms. We then compute these higher-derivative terms explicitly for the type IIB string compactif…
Modulus stabilization of modular flavor models in Jordan frame supergravity
School of Physics, Zhengzhou University（郑州大学物理学院）
本文在 Jordan 标架超引力中，通过非最小标量-曲率耦合形式 $Φ(τ,\barτ)R$，结合模不变性、尺度因子正定性和 Kähler 度规正定性，约束标架函数及 Kähler 势，并研究从 Jordan 标架到 Einstein 标架变换后标量势的形状，发现其与普通单模稳定化机制不同，势能在 $i\infty$ 不动点处可能静止导致逃逸型真空，但可通过典型模 VEV 在大 $\Imτ$ 下稳定，最后数值讨论了简化场景下的模稳定化。
We study an extra flavor in the cascading SU((k+1)M)xSU(k M) gauge theory by adding probe D7-brane to the geometry. By finding a solution to the kappa-symmetry equation we establish that the D7-brane is mutually supersymmetric with the background everywhere on the baryonic branch of moduli space. We also discuss possible applications of this result.
We have investigated moduli stabilization leading to hierarchical supersymmetry breakdown in racetrack models with two moduli fields simultaneously present in the effective racetrack superpotential. We have shown that stabilization of moduli occurs when a shift symmetry of the moduli space becomes gauged. This gauging results in a D-term contribution to the scalar potential that depends on moduli scalars. To break supersymmetry at a minimum created this way in the case where only a single combination of moduli is present in the superpotential one needs supergravity corrections. If the superpot…
Supersymmetric Moduli Space and Vacua with Vector Fields in $D=4$ Gauged $\mathcal{N}=8$ Supergravity
Universidad de Concepción（康塞普西翁大学）；UNESP-Universidade Estadual Paulista（圣保罗州立大学）；Politecnico di Torino（都灵理工大学）；INFN, Sezione di Torino（意大利国家核物理研究所都灵分部）；Universidade de Santiago de Compostela（圣地亚哥德孔波斯特拉大学）
We argue for the quantum-gravitational inconsistency of certain 6d $\mathcal{N}=(1,0)$ supergravity theories, whose anomaly-free gauge algebra $\mathfrak{g}$ and hypermultiplet spectrum $M$ were observed in arxiv:2012.01437 to be realizable only as part of a larger gauge sector $(\mathfrak{g}' \supset \mathfrak{g}, M' \supset M)$ in F-theory. To detach any reference to a string theoretic method of construction, we utilize flavor symmetries to provide compelling reasons why the vast majority of such $(\mathfrak{g},M)$ theories are not compatible with quantum gravity constraints, and how the "au…
Taking into account the recently proposed poly-instanton corrections to the superpotential and combining the race-track with a KKLT respectively LARGE Volume Scenario in an intricate manner, we show that we gain exponential control over the parameters in an effective superpotential. This allows us to dynamically stabilise moduli such that a conventional MSSM scenario with the string scale lowered to the GUT scale is realised. Depending on the cycles wrapped by the MSSM branes, two different scenarios for the hierarchy of soft masses arise. The first one is a supergravity mediated model with M_…
In this note, we prove that for all five-dimensional supergravities arising from M-theory compactified on a Calabi-Yau threefold, points of vanishing gauge coupling lie at infinite distance in the moduli space. Conversely, any point at infinite distance in the vector multiplet moduli space is a point of vanishing gauge coupling. This agrees with expectations from the Tower/Sublattice Weak Gravity Conjecture, the Swampland Distance Conjecture, and the Emergence Proposal.
The three-year data from WMAP are in stunning agreement with the simplest possible quadratic potential for chaotic inflation, as well as with new or symmetry-breaking inflation. We investigate the possibilities for incorporating these potentials within supergravity, particularly of the no-scale type that is motivated by string theory. Models with inflation driven by the matter sector may be constructed in no-scale supergravity, if the moduli are assumed to be stabilised by some higher-scale dynamics and at the expense of some fine-tuning. We discuss specific scenarios for stabilising the modul…
The dimensional reduction of eleven dimensional supergravity on a Calabi-Yau manifold gives N=2 supergravity in five dimensions with $h_{1,1}$ vector and $h_{2,1}+1$ hypermultiplets. In this paper instanton solutions are constructed which are responsible for nonperturbtative corrections to the hypermultiplet moduli spaces. These instantons are wrapped Euclidean membranes and fivebranes. For vanishing fivebrane charge the BPS conditions for these solutions define a flow in the hypermultiplet moduli space and are isomorphic to the attractor equations for four dimensional black holes.
We study the embedding of flat BPS 3-branes in five dimensional N=2 supergravity theory. We derive the branes' dynamical equations as well as general expressions for the hypermultiplet fields then focus on a single brane and study its time evolution. It is shown that the brane's Hubble parameter correlates with the moduli of the underlying manifold's complex structure. For certain particular solutions, the moduli seem to exhibit an instability; being large valued at early times then rapidly decaying to either zero or some convergent constant value. The possibility of extending these results to…
It is shown that the supergravity moduli spaces of D1-D5 and D2-D6 brane systems coincide with those of the Coulomb branches of the associated non-abelian gauge theories. We further discuss situations in which worldvolume brane actions include a potential term generated by probing certain supergravity backgrounds. We find that in many cases, the appearance of the potential is due to the application of the Scherk-Schwarz mechanism. We give some examples and discuss the existence of novel supersymmetric brane configurations.
We consider the moduli space of 1/2 BPS configurations of type IIB SUGRA found by Lin, Lunin and Maldacena (hep-th/0409174), and quantize it directly from the supergravity action, around any point in the moduli space. This quantization is done using the Crnkovic-Witten-Zuckerman covariant method. We make some remarks on the applicability and validity of this general on-shell quantization method. We then obtain an expression for the symplectic form on the moduli space of LLM configurations, and show that it exactly coincides with the one expected from the dual fermion picture. This equivalence …
We perform a complete classification of the flux-induced 12d algebras compatible with the set of N=1 type II orientifold models that are T-duality invariant, and allowed by the symmetries of the T^6/(Z_2 x Z_2) isotropic orbifold. The classification is performed in a type IIB frame, where only H_3 and Q fluxes are present. We then study no-go theorems, formulated in a type IIA frame, on the existence of Minkowski/de Sitter (Mkw/dS) vacua. By deriving a dictionary between the sources of potential energy for the three moduli (S, T and U) in types IIA and IIB, we are able to combine algebra resul…
We construct extremal, spherically symmetric black hole solutions to 4D supergravity with charge assignments that preclude BPS-saturation. In particular, we determine the ground state energy as a function of charges and moduli. We find that the mass of the non-BPS black hole remains that of a marginal bound state of four basic constituents throughout the entire moduli space and that there is always a non-zero gap above the BPS bound.
We consider the gravity-mediated SUSY breaking within the effective theory of six-dimensional brane-world supergravity. We construct the supersymmetric bulk-brane action by Noether method and find the nontrivial moduli coupling of the brane F- and D-terms. We find that the low energy Kahler potential is not of sequestered form, so gravity mediation may occur at tree level. In moduli stabilization with anomaly effects included, the scalar soft mass squared can be positive at tree level and it can be comparable to the anomaly mediation.
We describe methods for building "semi-realistic" models of F-term inflation. By semi-realistic we mean that they are built in, and obey the requirements of, "semi-realistic" particle physics models. The particle physics models are taken to be effective supergravity theories derived from orbifold compactifications of string theory, and their requirements are taken to be modular invariance, absence of mass terms and stabilization of moduli. We review the particle physics models, their requirements and tools and methods for building inflation models.
