Twisted compactification of N = 2 5D SCFTs to three and two dimensions from F(4) gauged supergravity
JHE
Twisted compactification of N
with E 0 1 2 3
∼ SU 0 1 2 3
symmetry. 0 1 2 3
0 254 Phayathai Road, Pathumwan , Bangkok 10330 , Thailand
1 Chulalongkorn University
2 String Theory and Supergravity Group, Department of Physics, Faculty of Science
3 Open Access , c The Authors
We study supersymmetric AdS4 × Σ2 and AdS3 × Σ3 solutions in half-maximal gauged supergravity in six dimensions with SU(2)R × SU(2) gauge group. The gauged supergravity is obtained by coupling three vector multiplets to the pure F (4) gauged supergravity. The SU(2)R R-symmetry together with the SO(3) ∼ SU(2) symmetry of the vector multiplets are gauged. The resulting gauged supergravity admits supersymmetric AdS6 critical points with SO(4) ∼ SU(2) × SU(2) and SO(3) ∼ SU(2)diag symmetries. The former corresponds to five-dimensional N = 2 superconformal field theories (SCFTs) We find new classes of supersymmetric AdS4 × Σ2 and AdS3 × Σ3 solutions with Σ2,3 being S2,3 and H2,3. These solutions describe SCFTs in three and two dimensions obtained from twisted compactifications of the aforementioned five-dimensional SCFTs with different numbers of unbroken supersymmetry and various types of global symmetries. ArXiv ePrint: 1507.01515
Gauge-gravity correspondence; AdS-CFT Correspondence; Supergravity
-
2 5D
SCFTs to
three and two dimensions from
F (4) gauged
supergravity
1 Introduction 2 3 4
AdS4 critical points
AdS3 critical points
Matter coupled N
A Supersymmetric AdS6 critical points and holographic RG flows
Introduction
Field theories in six and five dimensions have been shown to posses non-trivial conformal
not well understood as their lower dimensional analogues. The study of five-dimensional
SCFTs using the AdS/CFT correspondence [3] has attracted a lot of attention both from
ten and six-dimensional point of views, see for example [4–9]. And recently, the
investigation of supersymmetric AdS6 solutions has been carried out systematically in [10–12].
An approach to understand higher dimensional field theories is to make some
compactification of these theories to lower dimensions. The resulting lower dimensional field
and the holographic study via the AdS/CFT correspondence is still applicable at least in
the large N limit [13]. From string/M theory point of view, these twisted field theories
can be interpreted as wrapped branes on certain curved manifolds. In many cases, there
is a description in terms of lower dimensional gauged supergravities. In particular, for the
F (4) gauged supergravity and its matter-coupled version [14].
In this work, we will explore some aspects of twisted compactifications of
fivedimensional SCFTs within the framework of half-maximal gauged supergravity in six
dimensions coupled to matter multiplets [15, 16]. A similar study in the pure F (4) gauged
solutions have been identified along with their possible dual field theories. We will
further investigate solutions of this type in the matter-coupled F (4) gauged supergravity.
This could presumably give rise to more general solutions than those given in [18]. The
result would also provide new solutions describing IR fixed points of the RG flows from
SCFTs in five dimensions to three and two-dimensional SCFTs with different numbers of
As a starting point, we add three vector multiplets to the F (4) gauged supergravity
the R-symmetry group. AdS6 vacua of this theory including possible holographic RG flows
between the dual SCFTs and RG flows to non-conformal field theories have already been
studied in [8] and [9]. From the result in [8], there are two supersymmetric AdS6 critial
points. Both of them preserve the full sixteen supercharges, but one of them, with
nonvanishing scalar fields, break the full SU(2)R × SU(2) symmetry to its diagonal subgruop.
AdS/CFT correspondence.
being S2,3 or H2,3 with different residual symmetries. The resulting solutions would be
dual to SCFTs in three and two dimensions obtained from twisted compactifications of the
above mentioned five-dimensional SCFTs. These will give new AdS4 and AdS3 solutions
the holographic study of gauge theories in five and lower dimensions.
The paper is organized as follow. We give a brief review of the F (4) gauged supergravity
coupled to three vector multiplets in section 2. Possible supersymmetric AdS4 and AdS3
solutions are given in section 3 and 4, respectively. In section 5, we give some conclusions
and comments about the results. We also include an appendix describing supersymmetric
AdS6 critical points previously found in [8] as well as an analytic RG flow between them.
group. This gauged supergravity can be obtained by coupling three vector multiplets to
the pure F (4) gauged supergravity constructed in [17]. The full construction by using
the superspace approach can be found in [15, 16]. Apart from different metric signature
multiplet given by
and three vector multiplets with the field content
= 0, . . . , 5 and a, b = 0, . . . , 5. eaμ and
multiplet. Three of these vector fields wi (...truncated)