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SUMMARY:*Cancelled* - Loops in AdS: From the Spectral Representation to Po
sition Space
DTSTART;VALUE=DATE-TIME:20191112T130000Z
DTEND;VALUE=DATE-TIME:20191112T150000Z
DTSTAMP;VALUE=DATE-TIME:20191206T225306Z
UID:indico-event-861334@indico.cern.ch
DESCRIPTION:We compute a family of scalar loop diagrams in AdS. We use the
spectral representation to derive various bulk vertex/propagator identiti
es\, and these identities enable to reduce certain loop bubble diagrams to
lower loop diagrams\, and often to tree-level exchange or contact diagram
s. An important example is the computation of the finite coupling 4-point
function of the large-N conformal O(N) model on AdS3. Remarkably\, the re-
summation of bubble diagrams is equal to a certain contact diagram: the D
(1\,1\, 3/2 \, 3/2 (z\, zbar) function. Another example is a scalar with
φ^4 or φ^3 coupling in AdS3: we compute various 4-point (and higher poin
t) loop bubble diagrams with alternating integer and half-integer scaling
dimensions in terms of a finite sum of contact diagrams and tree-level exc
hange diagrams. The 4-point function with external scaling dimensions diff
erences obeying ∆12 = 0 and ∆34 = 1 enjoys significant simplicity whic
h enables us to compute in quite generality. For integer or half-integer s
caling dimensions\, we show that the M-loop bubble diagram can be written
in terms of Lerch transcendent functions of the cross-ratios z and zbar. F
inally\, we compute 2-point bulk bubble diagrams with endpoints in the bul
k\, and the result can be written in terms of Lerch transcendent functions
of the AdS chordal distance. We show that the similarity of the latter tw
o computations is not a coincidence\, but arises from a vertex identity be
tween the bulk 2-point function and the double-discontinuity of the bounda
ry 4-point function.\n\nhttps://indico.cern.ch/event/861334/
LOCATION:CERN 4/3-006 - TH Conference Room
URL:https://indico.cern.ch/event/861334/
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