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Gauge Fixing Problem in Cubic Superstring Field Theory

Gauge Fixing Problem in Cubic Superstring Field Theory. Masaki Murata YITP based on work in progress with Taichiro Kugo, Maiko Kohriki, Hiroshi Kunitomo and Isao Kishimoto. 1. Introduction 2. Gauge Fixing of Ramond Field 3. Gauge Fixing of Neveu-Schwarz Field (incomplete) 4. Other topic

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Gauge Fixing Problem in Cubic Superstring Field Theory

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  1. Gauge Fixing Problem in Cubic Superstring Field Theory Masaki Murata YITP based on work in progress with Taichiro Kugo, Maiko Kohriki, Hiroshi Kunitomo and Isao Kishimoto 1. Introduction 2. Gauge Fixing of Ramond Field 3. Gauge Fixing of Neveu-Schwarz Field (incomplete) 4. Other topic 5. Future directions Oct. 22, 2010 at YITP, Kyoto

  2. 1. Introduction(SSFT) Open Superstring Field Theories (SSFT)

  3. 1. Introduction(Motivation) Our goal is write down Siegel gauge action with kinetic operator L0 (F0) take into account of interaction terms Batalin-Vilkovisky (BV) formalism

  4. 1. Introduction (Batalin-Vilkovisky ) standard BV formalism field anti-field BV master equation Boundary condition gauge invariant action BV formalism with "Gauge-Fixed basis" Definition of and are different BV master equation Boundary condition gauge fixed action

  5. 1. Introduction (BV for bosonic SFT) Benefit of gauge-fixed basis : action satisfying master equation is same form as original :Ghost number constraint is relaxed. field anti-field BRST transformation: Siegel gauge

  6. 2. Gauge Fixing of Ramond (1) Kinetic term picture changing operator Kernel of Y : Additional gauge symmetry [Arefeva-Medvedev (1988)] [Kugo,Terao (1988)] Projection operator removing kernel of Y : ,

  7. 2. Gauge Fixing of Ramond (2) constrained field Projected field [Kazama-Neveu-Nicolai-West(1986)] We can rewrite the action as [Sazdovic(1987)] BV master equation Relax ghost number constraint of BRST transformation

  8. 2. Gauge Fixing of Ramond (3) Variation of action we don't have Y0 !! field anti-field Siegel gauge :

  9. 3. Gauge fixing of NS (PTY) [Preitschopf-Thorn-Yost(1990)], [Arefeva-Medvedev-Zubarev(1990)] -2, 0-picture PTY projection operator gauge Propagator

  10. 3. Gauge fixing of NS (PTY) is problematic : doesn’t have Klein-Gordon operator (second derivative) retracts (part of) world sheet extend the worldsheet retract the worldsheet t We would like to write down Siegel gauge action with kinetic operator L0 (F0) We haven't succeeded yet. I will show our trials to explain where difficulties come form.

  11. 3. Gauge Fixing of NS 1. Constructed another projection operator (1) Ramond naive extension NS We can show

  12. 3. Gauge Fixing of NS Ramond Projected field with The computation is much complicated. Ramond NS We couldn't find counterpart

  13. 3. Gauge Fixing of NS 2.Construct another projection operator (2) seems to be important : difficult to find We investigated another projection operator so that we can find We found one example by slightly modifying PTY's

  14. 3. Gauge Fixing of NS We found However, kinetic operator does not contain

  15. 4. Another topic modified cubic SSFT has divergence We searched another candidate of picture changing operator with no divergence Strategy : construct operators satisfying following conditions 1. 2. (Virasoro) primary, 3. commutes with BRST charge, Result : we proved uniqueness of X and Y study operators with different picture number

  16. 5.Future directions 1. Investigate gauge transformation at linearized level The computation is much complicated. original gauge transformation By straightforwardly calculating , we can specify what gauge is possible. The components eliminated by might be identified as anti-fields. This will make the calculation of simpler.

  17. 5. Future directions 2. “Minimal BRST-closed space” messy We want to construct the simpler projected state. “minimal BRST-closed space” for example let us consider Ramond sector minimal : the number of independent component is minimum BRST-closed : We want to construct simpler projected space as minimal BRST-closed space.

  18. 5. Future directions Minimal BRST-closed space for Ramond Start line Second step Close projected space can be expressed as minimal space!!

  19. 5. Future directions We want to construct ``minimal space’’ for NS Ramond NS ``zero modes'' First step ?

  20. These two formalisms can be related through anti-canonical transformation

  21. 5. Future directions 2. “Minimal BRST-closed space” we can express any state in terms of minimal : the number of independent is minimum BRST-closed : Iterative construction : V

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