6D双重共形对称性和AdS中的最小体积资源-CSDN文库

Open

Access

46 浏览量 2020-03-27 12:30:09 上传评论收藏 652KB PDF 举报

资源推荐

资源详情

资源评论

JHEP12(2016)105

Published for SISSA by Springer

Received: November 16, 2016

Revised: December 8, 2016

Accepted: December 12, 2016

Published: December 20, 2016

6d dual conformal symmetry and minimal volumes

in AdS

Jyotirmoy Bhattacharya and Arthur E. Lipstein

Centre for Particle Theory & Department of Mathematical Sciences, Durham University,

South Road, Durham DH1 3LE, United Kingdom

E-mail: jyotirmoy.bhattacharya@durham.ac.uk,

arthur.lipstein@durham.ac.uk

Abstract: The S-matrix of a theory often exhibits symmetries which are not manifest

from the viewpoint of its Lagrangian. For instance, powerful constraints on scattering

amplitudes are imposed by the dual conformal symmetry of planar 4d N = 4 super Yang-

Mills theory and the ABJM theory. Motivated by this, we investigate the consequences

of dual conformal symmetry in six dimensions, which may provide useful insight into the

worldvolume theory of M5-branes (if it enjoys such a symmetry). We ﬁnd that 6d dual

conformal symmetry uniquely ﬁxes the integrand of the one-loop 4-point amplitude, and

its structure suggests a Lagrangian with more than two derivatives. On integrating out

the loop momentum in 6 − 2 dimensions, the result is very similar to the corresponding

amplitude of N = 4 super Yang-Mills theory. We conﬁrm this result holographically by

generalizing the Alday-Maldacena solution for a minimal area string in Anti-de Sitter space

to a minimal volume M2-brane ending on a pillow-shaped surface in the boundary whose

seams correspond to a null-polygon. This involves careful treatment of a prefactor which

diverges as 1/, and we comment on its possible interpretation. We also study 2-loop 4-

point integrands with 6d dual conformal symmetry and speculate on the existence of an

all-loop formula for the 4-point amplitude.

Keywords: AdS-CFT Correspondence, M-Theory, p-branes, Scattering Amplitudes

ArXiv ePrint: 1611.02179

Open Access,

 The Authors.

Article funded by SCOAP

doi:10.1007/JHEP12(2016)105

JHEP12(2016)105

for M2-branes [8]. The key insight was to perform a Z

orbifold of the space transverse to

the branes which breaks 1/4 of the susy when k > 2, but allows one to deﬁne a tunable

coupling for the theory. The Lagrangian is a 3d superconformal Chern-Simons theory with

N = 6 susy known as the ABJM theory.

When the orbifold parameter is large, it is dual

to IIA string theory on AdS

×CP

The third example is the least understood because the worldvolume theory describing

multiple M5-branes remains elusive. The M5-brane theory is not only crucial for under-

standing AdS/CFT and M-theory, it also provides the geometric origin of electric-magnetic

duality of many supersymmetric theories that arise from dimensional reduction [12–14]. It

is believed to be a 6d CFT whose ﬁeld content is a (2, 0) tensor multiplet, which consists

of a self-dual two-form gauge ﬁeld, ﬁve scalars, and eight fermions. Although the worldvol-

ume theory for a single M5-brane is well-understood [15, 16], it is unclear how to generalize

it to more than one. In the absence of a tunable coupling, it is not clear whether such a

theory would even admit a Lagrangian description (see [17–24] for some attempts in this

direction).

Using modern methods for computing on-shell scattering amplitudes, it is possible

to learn a great deal about the S-matrix of many theories without reference to their La-

grangians. Moreover, the S-matrix often exhibits symmetries that are totally obscure

from the point of view of the Lagrangian. For example, the planar amplitudes of N = 4

SYM [25–27] and the ABJM theory [28–30] exhibit a remarkable property known as dual

conformal symmetry in the planar limit. In the context of N = 4 SYM, the dual confor-

mal symmetry can be understood as the ordinary conformal symmetry of a dual Wilson

loop whose contour is obtained by arranging the external momenta of the amplitude head

to tail [31–36]. Moreover, the amplitude/Wilson loop duality of 4d N = 4 SYM can be

derived from the self-duality of IIB string theory under a certain combination of bosonic

and fermionic T-duality transformations [37, 38]. In the case of ABJM theory, the am-

plitude/Wilson loop duality does not generalize beyond 4-points and the status of the

fermionic T-duality in the gravity dual is also unclear [39–41]. Hence, the origin of dual

conformal symmetry in the ABJM theory appears to be rather mysterious.

Note that dual conformal symmetry is not equivalent to ordinary superconformal sym-

metry and when the two are combined, they give rise to inﬁnite dimensional Yangian

symmetry for scattering amplitudes [42, 43]. Hence, dual conformal symmetry imposes

very powerful constraints on the planar S-matrix. For example, in N = 4 SYM and ABJM

one can use dual conformal symmetry to uniquely ﬁx the 1-loop 4-point integrand, from

which the 4-point tree-level amplitudes can be deduced using unitarity methods [44, 45].

The rest of the tree-level S-matrix can then be deduced using BCFW recursion [46], which

in principle can be used to deduce the Lagrangian. Hence, apriori if we had no idea how to

formulate ABJM or N = 4 SYM, we could have deduced these theories simply by looking

for dual conformal invariant S-matrices in 3d and 4d, respectively.

At loop-level, dual conformal symmetry is broken by IR divergences but the four and

ﬁve points amplitudes of N = 4 SYM are nevertheless ﬁxed to all orders by an anomalous

Prior to the ABJM theory, there were other proposals which have maximal superconformal symmetry,

although the interpretation of these theories is not fully understood [9–11].

– 2 –

JHEP12(2016)105

dual conformal Ward identity [47]. These all-loop formulae, ﬁrst conjectured by Bern,

Dixon, and Smirnov [48], boil down to exponentiating the one-loop amplitude and encoding

the coupling dependence through the cusp and collinear anomalous dimensions. This has

been conﬁrmed up to four loops in perturbation theory [49–51], as well as at strong coupling

using string theory [31, 52, 53]. There is also evidence that a similar all-loop formula exists

for the 4-point amplitude of the ABJM theory [54–60]. In particular, the 2-loop 4-pt

amplitude of the ABJM theory has an almost identical structure to the 1-loop 4-point

amplitude of N = 4 SYM, and the strong coupling calculation in the dual string theory is

identical to that of N = 4 SYM at leading order.

Given the important role played by dual conformal symmetry in the ﬁrst two examples

of the AdS/CFT duality described above, in this note we proceed to explore its implications

for the theory of M5-branes, assuming it enjoys such a symmetry. There are of course,

several subtleties with this point of view. For instance, it has previously been shown

that is not possible to construct a tree-level S-matrix for (2, 0) tensor multiplets assuming

locality and unitarity [61]. On the other hand, since the (2, 0) theory is strongly coupled,

it is unclear what the asymptotic states should be. In this note, we will not make any

assumptions about the asymptotic states, locality, or even the superconformal symmetry

of the theory. Our only assumptions will be that the theory admits something analogous

to a planar limit where a semi-classical supergravity description is admissible in the bulk,

and that it has rational loop integrands

which exhibit dual conformal symmetry in six

dimensions.

In this note, we ﬁnd that 6d dual conformal symmetry ﬁxes the 1-loop 4-point in-

tegrand. Like N = 4 SYM, the integrand can be associated with a scalar box diagram

with massless external legs, but unlike N = 4 SYM, some of the propagators are squared

which suggests an underlying Lagrangian with more than two derivative. We also con-

sider triangle and bubble diagrams with dual conformal integrands but show that they are

not important at 4 points. Remarkably, although the 4-point 1-loop integrand that we

obtain has a very diﬀerent spacetime structure than that of N = 4 SYM, its integral is

essentially the same (up to scheme-dependent terms). Recalling that a very similar struc-

ture was found for the 2-loop 4-point amplitude of the ABJM theory, it therefore appears

that 4-point amplitudes with dual conformal symmetry have a universal structure. We

also carry out a preliminary analysis of 2-loop 4-point integrands consistent with 6d dual

conformal symmetry and unitarity. Remarkably, although these integrands have a very

diﬀerent spacetime structure than that of N = 4 SYM, their Mellin-Barnes representation

is very similar, suggesting that the similarity to N = 4 SYM might extend beyond 1-loop.

The all-loop formula for the four-point amplitude of N = 4 SYM was ﬁrst conﬁrmed

at strong coupling by Alday and Maldacena who computed the minimal area of a string

in AdS whose boundary corresponds to the null polygon obtained by arranging the ex-

Since the M5-brane theory is self-dual, it is unclear how to deﬁne a topological expansion in terms of an

’t Hooft parameter. A similar diﬃculty occurs for the M2-brane theory, but can be overcome by orbifolding

the space transverse to the branes, which introduces a tunable coupling.

Note that 6d (1, 1) SYM amplitudes have dual conformal symmetry in the four-dimensional sense [62],

as do maximal SYM amplitudes in 10d [63] and 3d [64].

– 3 –

剩余23页未读，继续阅读

评论收藏

内容反馈

weixin_38515573

粉丝: 8
资源: 940

6D双重共形对称性和AdS中的最小体积

关于6D超共形场论的整体对称性

Wald熵和6d共形异常

AdS3×S3树级相关器：隐藏的六维共形对称性

分类6D SCFT的整体对称性

6d SCFT和U（1）风味对称性

6D SCFT和5D理论的阶段

关于AdS7真空和6D SCFT的SUSY打破模空间

7D爱因斯坦和6D共形引力中的一环发散

在六个维度上最小化共形超重力的不变量

附录：通过6d SCFT对5d SCFT进行分类：排名第一

B型异常匹配和6D（2,0）理论

4d Spin（n）规范理论的对称性增强和6d的压缩

6D分数量子霍尔效应

KUKA机器人示教器禁用6D鼠标的具体方法演示.docx

具有保形物质的4D量规理论

6D位姿估计 综述文献总结

异常流入，意外对称和自发对称破坏

jpeg6d编译后库

6d SCFT，5d对偶和Tao网络图

佳能6D 1.16固件 用于刷魔灯

奇异椭圆Calabi-Yau 3折和最小6d SCFT的拓扑字符串

通过5d个实例，q W $$ q \ mathcal {W} $$-代数和（1，0）超共形索引的对称性增强

佳能6D 1.1.6版本固件 支持魔灯插件, 亲测可用.

6d的S 4×SU（5）SUSY GUT

LSM6DS3计步、加速度、6D\4D传感器驱动代码及中文参考手册

ndi 6D Architect

6d理论的双重红外极限

最新资源

6D位姿估计综述文献总结

佳能6D 1.16固件用于刷魔灯

佳能6D 1.1.6版本固件支持魔灯插件, 亲测可用.