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SUMMARY:Igor R. Klebanov (Professor\, Princeton University\, USA)
DTSTART:20200615T133000Z
DTEND:20200615T153000Z
DTSTAMP:20260423T011048Z
UID:QASTM/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QASTM/11/">B
 reaking of Discrete and Continuous Symmetries in SYK-like Models</a>\nby I
 gor R. Klebanov (Professor\, Princeton University\, USA) as part of Quantu
 m Aspects of Space-Time and Matter\n\n\nAbstract\nA Majorana fermion is th
 e most elemental quantum degree of freedom – a pair of them has only two
  quantum states. Yet\, a large number of fermions with interactions coupli
 ng four of them at a time can exhibit interesting quantum dynamics. Models
  of this kind include the Sachdev-Ye-Kitaev (SYK) model\, where the coeffi
 cients of quartic interactions are randomly distributed\, and the Tensor m
 odels\, where they respect continuous symmetries. These models exhibit app
 roximate invariance under scaling of the time and have power law fall-off 
 of the correlation functions. In this talk we will discuss a pair of SYK o
 r Tensor models coupled by the quartic interactions\, and show that they p
 roduce a richer set of phenomena. These include a line of fixed points\, w
 here critical exponents vary along the line and formally acquire imaginary
  parts outside it. For one sign of the coupling constant\, the approximate
  scale invariance continues to hold. For the other\, a gap opens in the en
 ergy spectrum\, resulting in exponential fall-off of correlation functions
 . This is indicative of breaking of a discrete symmetry. Thus\, our quantu
 m mechanical model exhibits dynamical phenomena characteristic of higher d
 imensional quantum field theories. Furthermore\, the gapped phase of our m
 odel may be dual to a certain traversable wormhole in two-dimensional spac
 e-time. The talk will end with a similar discussion of a pair of complex S
 YK models coupled by a quartic interaction which preserves the U(1) x U(1)
  symmetry. For a range of parameters\, this model gives rise to breaking o
 f one of the U(1) symmetries. This is demonstrated via an analysis of the 
 large N Dyson-Schwinger equations\, as well as by Exact Diagonalizations o
 f the finite N Hamiltonians.\n
LOCATION:https://researchseminars.org/talk/QASTM/11/
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