A requiem forAdS4×CP3fermionic self-T duality

Abstract

Strong evidence for dual superconformal symmetry in N = 6 superconformal Chern-Simons theory has fueled expectations that the AdS/CFT dual geometry AdS4 × CP 3 is self-dual under T-duality. We revisit the problem to identify commuting bosonic and fermionic isometries in a systematic fashion and show that fermionic T-duality, a symmetry originally proposed by Berkovits & Maldacena, inevitably leads to a singularity in the dilaton transformation. We show that TsT deformations commute with fermionic T-duality and comment on T-duality in the corresponding sigma model. Our results rule out self-duality based on fermionic T-duality for AdS4 × CP 3 or its TsT deformations, but leave the door open for new possibilities. INTRODUCTIONThe AdS/CFT correspondence is best understood as an equivalence between N = 4 super Yang-Mills (sYM) and type IIB string theory on AdS 5 × S 5 [1]. New ideas incubated in this unique setting quickly percolate to less familiar forms of the duality, where generality may be tested. A duality between superconformal N = 6 ChernSimons (ABJM) theory and type IIA superstrings on AdS 4 × CP 3 [2] represents the first challenge.For AdS 5 /CFT 4 , it is well-known that integrability is present in the planar limit of N = 4 sYM and also strings on AdS 5 × S 5 [3,4], allowing one to connect perturbative regimes of both descriptions. Integrability is believed to play a substantial rôle in relations between scattering amplitudes and Wilson loops [5][6][7][8], as well as the emergence of a hidden superconformal symmetry [9], whose closure with the original superconformal symmetry leads at tree level to Yangian symmetry [10,11], a recognisable integrable structure. Moreover, this so-called "dual superconformal symmetry" can be traced back to a selfmapping of the geometry AdS 5 ×S 5 under a combination of bosonic and fermionic T-dualities [12][13][14].Subsequent developments for ABJM theory largely parallel N = 4 sYM. Integrability is again a feature of the planar limit [15,16] and string theory on AdS 4 ×CP 3 [17][18][19][20]. Moreover, perturbative calculations provide convincing evidence for amplitude/Wilson loop duality [21,22], dual superconformal [23][24][25][26] and Yangian symmetry [27,28]. The similarities between AdS 5 /CFT 4 and AdS 4 /CFT 3 duality are striking and led to the hope that a self-dual mapping of the geometry AdS 4 × CP 3 under a combination of bosonic and fermionic T-dualities could also account for the observed perturbative symmetries in ABJM theory. In this letter we show that the Berkovits-Maldacena transformation [13] inevitably leads to a singularity in the dilaton shift, so self-duality based on fermionic T-duality can not work for AdS 4 × CP 3 .This result may come as no great surprise, since we have witnessed a number of no-go results of varying rigour [29][30][31][32][33][34]. Despite this, none are completely satisfactory. Earlier statements, e. g. [29,30], fail to take account of the chirality and the results of ref. [32], whose approach we follow, fail to be comprehensive in...

Noncommutative massive unquenched ABJM

“…At the level of field theory, the non-commutative ABJM model has been recently studied in perturbation theory in [28], whereas its gravity dual has been obtained using string dualities in [29]. Interestingly, it was pointed out later in [30] that this particular TsT-duality will preserve the same amount of supersymmetry as the ambient commutative theory.…”

ABJM flux-tube and scattering amplitudes

“…We can probe more of the pentagon transitions by considering the heptagon WL, shown in the right panel of figure 5. After modding out by the pentagons and squares in the sequence, the OPE ratio reads 34) with the restriction to the 3d kinematics corresponding to φ 1,2 = 0. According to [85], the remainder function R 7 = 1 + O(g 3 ), and thus W 7 should match with the SYM answer to leading order at weak coupling ∼ g 2 .…”

“…The most important deviation from the SYM story, pertinent to our current consideration, is the absence of a well-established duality of scattering amplitudes in ABJM theory to a null-polygonal super-Wilson loop. This can be traced back to the lack of the fermionic T-self-duality of the AdS 4 ×CP 3 background [34], see also [35][36][37][38]. If exists, it would imply by default the dual superconformal symmetry.…”

T-duality to scattering amplitude and Wilson loop in non-commutative super Yang-Mills theory

“…On the other hand, many works about the fermionic T-duality transform and the scattering amplitude/Wilson loop duality have been done in the past years [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] 4 . One of the purposes of the present work is to present the construction of fermionic T-duality transformation of the NCAdS background to cancel the non-constant dilaton and the complex field strength, and corresponding string solutions in the final dual background in more details which are expected to dual to scattering amplitude.…”

“…In sec.2, we first review the TsT transformation of 3 See [20] for a special scattering amplitudes amplitude in the finite temperature regime of non-commutative Tang-mills theory. 4 These works [21][22][23][24][25][26][27][28][29] are focus on the ABJM theory and the other works [30][31][32][33][34][35] study the N = 4 SYM theory.…”