Comments on the Stability of SUSY Theories Jean-Fran cois Fortin - PowerPoint PPT Presentation

Preliminaries Faith of the False Vacuum Implications for SUSY Theories Conclusions Comments on the Stability of SUSY Theories Jean-Fran¸ cois Fortin Department of Physics, University of California, San Diego La Jolla, CA May 10-12, 2010 Phenomenology 2010 Symposium based on arXiv:0906.3714 [hep-th] (Tom Banks, JFF), work in progress (JFF)

Preliminaries Faith of the False Vacuum Implications for SUSY Theories Conclusions Outline Preliminaries 1 SUSY Breaking vs R -symmetry Breaking Faith of the False Vacuum without Gravity Faith of the False Vacuum 2 Faith of the False Vacuum with Gravity Implications for SUSY Theories 3 Temperature and Entropy of dS Space Stable dS space with N < ∞ Conclusions 4

Preliminaries Faith of the False Vacuum Implications for SUSY Theories Conclusions SUSY Breaking vs R -symmetry Breaking Spontaneous SUSY breaking in stable states → Exact R -symmetry Nelson, Seiberg - Unbroken exact R -symmetry ⇒ Massless gauginos not compatible with experimental constraints - Spontaneously broken exact R -symmetry ⇒ Massless R -axion not compatible with experimental constraints ⇒ Need explicit R -symmetry breaking

Preliminaries Faith of the False Vacuum Implications for SUSY Theories Conclusions SUSY Breaking vs R -symmetry Breaking Spontaneous SUSY breaking in metastable states → Approximate R -symmetry Intriligator, Seiberg, Shih - Approximate R -symmetry ⇒ SUSY states far in field space, metastability - Unbroken approximate R -symmetry ⇒ Massive gauginos from explicit R -symmetry breaking - Spontaneously broken approximate R -symmetry ⇒ Massive R -axion from explicit R -symmetry breaking Metastable SUSY breaking more generic than stable SUSY breaking ⇒ Metastable SUSY breaking with tunneling probability Γ / V compatible with experimental constraints

Preliminaries Faith of the False Vacuum Implications for SUSY Theories Conclusions Faith of the False Vacuum without Gravity Tunneling probability Γ / V = Ae − [ S E ( φ ) − S E ( φ F )] Coleman - Euclidean action for the instanton solution S E ( φ ) - Vanishing background Euclidean action S E ( φ F ) = 0

Preliminaries Faith of the False Vacuum Implications for SUSY Theories Conclusions Faith of the False Vacuum without Gravity Tunneling probability Γ / V = Ae − [ S E ( φ ) − S E ( φ F )] Coleman - Euclidean action for the instanton solution S E ( φ ) - Vanishing background Euclidean action S E ( φ F ) = 0

Preliminaries Faith of the False Vacuum Implications for SUSY Theories Conclusions Faith of the False Vacuum with Gravity Tunneling probability Γ / V = Ae − [ S E ( φ ) − S E ( φ F )] Coleman, De Luccia - Background Euclidean action S M E ( φ F ) = 0 and S dS E ( φ F ) < 0 - Actual “decay” of metastable Minkowski space to AdS space ⇒ Gravitational collapse (Big Crunch) - Stability of seemingly metastable Minkowski space in thin-wall approximation

Preliminaries Faith of the False Vacuum Implications for SUSY Theories Conclusions Faith of the False Vacuum with Gravity � � ǫ ≈ | ∆ φ | Space of potentials partitioned in the V F → 0 limit M P Aguirre, Banks, Johnson & Bousso, Freivogel, Lippert - Below the Great Divide ( ǫ < ǫ c ∼ O (1)) - Non-compact instanton - Instanton action scales like and comparable to background action ⇒ No “extra” decay suppression

Preliminaries Faith of the False Vacuum Implications for SUSY Theories Conclusions Faith of the False Vacuum with Gravity � � ǫ ≈ | ∆ φ | Space of potentials partitioned in the V F → 0 limit M P Aguirre, Banks, Johnson & Bousso, Freivogel, Lippert - Above the Great Divide ( ǫ > ǫ c ∼ O (1)) - Compact instanton - Instanton action negligible compared to background action ⇒ “Extra” decay suppression of order O ( e S dS E ( φ F ) )

Preliminaries Faith of the False Vacuum Implications for SUSY Theories Conclusions Temperature and Entropy of dS Space 1 2 π R dS and entropy S dS = π ( R dS M P ) 2 dS temperature T dS = Gibbons, Hawking E ( φ F ) = −S dS thus Γ / V = Ae − [ S E ( φ )+ S dS ] S dS Below the Great Divide Λ dS → 0 - Γ / V = Ae − [ S E ( φ )+ S dS ] − − − − → finite > 0 - Actual “decay” of metastable dS space to AdS space ⇒ Gravitational collapse (Big Crunch) - No entropic explanation of decay Above the Great Divide Λ dS → 0 → Ae −S dS ≈ 0 - Γ / V = Ae − [ S E ( φ )+ S dS ] − − − − - Decay seen as a Poincar´ e recurrence instead of an instability - Entropic explanation of decay

Preliminaries Faith of the False Vacuum Implications for SUSY Theories Conclusions Stable dS space with N < ∞ Quantum theory of stable dS space ⇒ Finite number of quantum states N < ∞ (Assumption) Banks, Fischler ⇒ Theory above the Great Divide

Preliminaries Faith of the False Vacuum Implications for SUSY Theories Conclusions Stable dS space with N < ∞ (Assumption) Consequences for models with SUSY breaking in M P → ∞ limit (e.g. gauge and gravity mediation) - Metastable SUSY breaking with SUSY vacua ⇒ AdS space theories with Λ AdS ≈ − F 2 / M 2 P - | ∆ φ | ≪ M P ⇒ Theory below the Great Divide ⇒ Spontaneous SUSY breaking in stable states ! - Generic with (spontaneously broken) exact R -symmetry P ) 1 / 4 > 10 MeV - PNGB R -axion with m a ≈ ( F 3 / M 2 Bagger, Poppitz, Randall √ F � 10 5 GeV - Gauge mediation ⇒ - Gravity mediation ⇒ Cosmologically safe R -axion with m a ≈ 10 7 GeV - Non-generic superpotential ⇒ Cosmological SUSY breaking Banks

Preliminaries Faith of the False Vacuum Implications for SUSY Theories Conclusions Stable dS space with N < ∞ (Assumption) Consequences for models with SUSY breaking in M P → ∞ limit (e.g. gauge and gravity mediation) - Metastable SUSY breaking with SUSY vacua ⇒ AdS space theories with Λ AdS ≈ − F 2 / M 2 P - | ∆ φ | ≪ M P ⇒ Theory below the Great Divide ⇒ Spontaneous SUSY breaking in stable states ! - Generic with (spontaneously broken) exact R -symmetry P ) 1 / 4 > 10 MeV - PNGB R -axion with m a ≈ ( F 3 / M 2 Bagger, Poppitz, Randall √ F � 10 5 GeV - Gauge mediation ⇒ - Gravity mediation ⇒ Cosmologically safe R -axion with m a ≈ 10 7 GeV - Non-generic superpotential ⇒ Cosmological SUSY breaking Banks

Preliminaries Faith of the False Vacuum Implications for SUSY Theories Conclusions Conclusions M P → ∞ limit - SUSY breaking and R -symmetry breaking ⇒ Spontaneous SUSY breaking in metastable states - Massive gauginos - Massive R -axion M P < ∞ - Stable dS space with N < ∞ (Assumption) ⇒ Spontaneous SUSY breaking in stable states - Generic with exact R -symmetry - Non-generic superpotential