M-theory and seven-dimensional inhomogeneous Sasaki-Einstein manifolds

Kim, Hyojoong; Kim, Nakwoo; Kim, Sun Chang; Lee, Jung Hun

doi:10.1007/jhep01(2011)075

Cited by 11 publications

(5 citation statements)

References 54 publications

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“…We can also apply to inhomogeneous Sasaki-Einstein manifolds, for example, Y p,k CP 2 [26,42]. The operator counting method was studied in [34] and successfully reproduced the volume of Y p,k CP 2 [50] using the AdS/CFT dictionary found in [51]. We expect that the monopole operator plays an important role in this case.…”

Section: Discussionmentioning

confidence: 95%

Black holes with baryonic charge and $$ \mathcal{I} $$ -extremization

Kim

2019

J. High Energ. Phys.

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Recently it was discovered that twisted superconformal index I can be used to understand the Bekenstein-Hawking entropy of magnetically charged black holes in AdS spacetime. In this paper we apply the so-called I-extremization procedure to threedimensional gauge field theories and their geometric dual, focusing in particular on the seven-dimensional Sasaki-Einstein manifold M 1,1,1 . We generalize recent studies on relations among toric geometry, variational principles, and black hole entropy to the case of AdS 2 × Y 9 , where Y 9 is a fibration of toric Sasaki-Einstein manifold M 1,1,1 over a twodimensional Riemann surface Σ g . The nine-dimensional variational problem is given in terms of an entropy functional. In order to illustrate the computations as explicitly as possible, we consider cases where either only mesonic or baryonic fluxes are turned on. By employing the operator counting method, we calculate the S 3 free energy and the topologically twisted index I at large-N . The result for I, it turns out, can be also obtained from the variational principle of the entropy functional with mesonic fluxes. We also study asymptotically AdS 4 black holes which are magnetically charged with respect to the vector field in the Betti multiplet. By extremizing the entropy functional with baryonic flux, we compute the entropy and find that it agrees with the entropy of an explicit solution in a four-dimensional gauged supergravity which is a consistent truncation of eleven-dimensional supergravity in AdS 4 × M 1,1,1 . arXiv:1904.05344v2 [hep-th]

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Section: Discussionmentioning

confidence: 95%

Black holes with baryonic charge and $$ \mathcal{I} $$ -extremization

Kim

2019

J. High Energ. Phys.

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“…Since this solution is BPS the classical quantities are exact at quantum level, and one can establish a mapping between the global charges in field theory and the angular momenta of the geodesic motion [33]. It turns out that x = 1 orbits are dual to the operators without the monopole operator.…”

Section: A Non-chiral Model : Dual Abjmmentioning

confidence: 96%

“…Because the quiver diagram Fig.4 does not have obvious symmetry other than flavor SU (3), it is not clear what is the right R-charge assignment. But it turns out that from classical particle motion one can read off simple relations between the R-charge of various fields [33]. We consider a particle moving along the Reeb vector direction, i.e.…”

Section: A Non-chiral Model : Dual Abjmmentioning

confidence: 99%

Operator counting for $ \mathcal{N} = {2} $ Chern-Simons gauge theories with chiral-like matter fields

Kim

2012

J. High Energ. Phys.

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Abstract:The localization formula of Chern-Simons quiver gauge theory on S 3 nicely reproduces the geometric data such as volume of Sasaki-Einstein manifolds in the large-N limit, at least for vector-like models. The validity of chiral-like models is not established yet, due to technical problems in both analytic and numerical approaches. Recently Gulotta, Herzog and Pufu suggested that the counting of chiral operators can be used to find the eigenvalue distribution of quiver matrix models. In this paper we apply this method to some vector-like or chiral-like quiver theories, including the triangular quivers with generic Chern-Simons levels which are dual to in-homogeneous Sasaki-Einstein manifolds Y p,k (CP 2 ). The result is consistent with AdS/CFT and the volume formula. We discuss the implication of our analysis.

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“…Figure 5(a) shows the presence of qualitatively new "horizontal solutions" in the r − n s plane. If we drop all the α-dependent terms in the scalar potential (9) except the global term linear in α (which is −8α κ s c 3 m 2 x 3 ), the number of horizontal solutions in this region increases. On the other hand, dropping this term and keeping the others does not…”

Section: B the Effect Of The Parameters On The Modelmentioning

confidence: 99%

“…This is somewhat disfavored, although it is within the 2σ bounds, n s = 0.971 ± 0.010 [5]. However, the addition of a linear soft-SUSY breaking term [6] reduces n s significantly [7]; this term is also important in explaining the MSSM µ-problem [8][9][10]. It has been shown that small gravity waves (tensor-to-scalar ratio r) are produced with minimal Kähler (retaining the lowest-order SUGRA term), radiative corrections, and positive soft mass squared and negative linear soft-SUSY breaking terms in the potential.…”

Section: Introductionmentioning

confidence: 99%

R-symmetry breaking in supersymmetric hybrid inflation

et al. 2013

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We consider a supersymmetric hybrid inflation scenario in which the U (1) R-symmetry is explicitly broken by Planck scale suppressed operators in the superpotential. We provide an example with minimal Kähler potential, with the R-symmetry breaking term relevant during inflation being αS 4 , where S denotes the well-known gauge singlet inflaton superfield. The inflationary potential takes into account the radiative and supergravity corrections, as well as the soft supersymmetry breaking terms. For successful inflation, with the scalar spectral index in the currently preferred range, n s ≈ 0.97 ± 0.010, |α| 10 −7 . The tensor to scalar ratio r 10 −4 , while |dn s /d ln k| ∼ O(10 −3 ) − O(10 −4 ).PACS numbers: 98.80.Cq INTRODUCTIONModern cosmology has seen rapid developments due to experiments such as COBE and WMAP. Augmenting their unprecedented successes will be Planck, which may for the first time yield direct evidence of inflation. At the same time, there are enormous strides being made in particle physics, with the LHC having made perhaps the greatest single discovery in the field in decades, while the testing of supersymmetry (SUSY) is highly anticipated. For the first time particle and cosmological models can be tested with precision, and the deep connections between these two fields motivate us to consider the effects that particle physics considerations have on inflationary models. This has led to models such as, among others, SUSY hybrid inflation.The standard version of SUSY hybrid inflation [1-3] remains one of the most successful and well-motivated inflationary models. It is the most general non-trivial model one can write with a gauge singlet field S and supermultiplets Φ andΦ that respects U (1) R , such that the latter two fields belong to non-trivial representations of the gauge group G. It has a connection to particle physics in that within it grand unified theories (GUTs) are naturally incorporated. In this model the gauge group G is broken to a subgroup H at the end of inflation, and the energy scale at which this occurs is related to local temperature anisotropies in the cosmic microwave background radiation [1]; this scale happens to be close to the GUT scale, indicating that G may be related to a GUT. In addition, supergravity (SUGRA) corrections remain under control [4] because this model can yield solutions within the WMAP nine-year 2σ bounds without trans-Planckian inflaton field values. In this model, where only (minimal) SUGRA and radiative corrections are added to the global potential, a numerical lower bound on the scalar spectral index, n s ≈ 0.985, develops. This is somewhat disfavored, although it is within the 2σ bounds, n s = 0.971 ± 0.010 [5]. However, the addition of a linear soft-SUSY breaking term [6] reduces n s significantly [7]; this term is also important in explaining the MSSM µ-problem [8][9][10]. It has been shown that small gravity waves (tensor-to-scalar ratio r) are produced with minimal Kähler (retaining the lowest-order SUGRA term), radiative corrections, and positi...

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M-theory and seven-dimensional inhomogeneous Sasaki-Einstein manifolds

Cited by 11 publications

References 54 publications

Black holes with baryonic charge and $$ \mathcal{I} $$ -extremization

Black holes with baryonic charge and $$ \mathcal{I} $$ -extremization

Operator counting for $ \mathcal{N} = {2} $ Chern-Simons gauge theories with chiral-like matter fields

R-symmetry breaking in supersymmetric hybrid inflation

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