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弦理論における準安定状態の崩壊
弦理論における準安定状態の崩壊 ーマルチバースの理解へ向けてー Aya Kasai and Yutaka Ookouchi (Kyushu U.) Semi-classical vacuum decay now, the previous vacuum is false. [ P. Steinhardt, `81] [Eto,Hamada,Kamada,Kobayashi,Ohashi,Ookouchi ’12] T r Speciality : 1) semi-classical 2) inhomogeneous 3) fussy soliton このアイディアを弦理論に輸入しよう！ 1) Vacuum instability via roll-over process plays crucial role in multiverse (life-time of vacua) 2) Bubble can be a giant monopole 3) Topology of a bubble may not be sphere Dielectric Brane Dielectric brane known as Myers effect naturally fits our studies Dielectric Brane Dielectric brane known as Myers effect naturally fits our studies Turning on RR-flux p=3 case Known as dielectric brane [Emparan 97, Myers 99, Hashimoto 02] キーポイント Dielectric brane known as Myers effect naturally fits our studies Bubble/soliton bound state corresponds to the dielectric brane! Example [Aganagic, Vafa et al 06] Type IIB theory compactified on Calabi-Yau Set up of geometry (manifold) when x is near a1 Looks like conifold rewrite the equations with vectors vector I lives on S3 vector R lives on S2 on the tangent space of the S3 r S2 r S3 S2 S3 back to the original geometry real part when we fix the xr to this submanifold looks like a S2 so, real part submanifold looks like a set of S2 a1 a2 a1 a2 [Aganagic et al ’06] Metastable vacuum D5 brane at a1 = N+n Anti D5 brane at a2 = n energy gap True vacuum → n pairs can annihilate D3 [Aganagic et al ’06] D3 brane wrapping on 3-chain [B] = stringy monopole DWD5 brane wrapping on 3-chain [B] = Domain wall 0 1 2 3 4 5 6 7 8 9 D3 ● × × × ● ● ● × × × dw ● D5 △ △ △ ● ● ● × × × 6 direction 6 direction 4,5 direction [Aganagic et al ’06] D3 brane wrapping on 3-chain [B] = stringy monopole DWD5 brane wrapping on 3-chain [B] = Domain wall 0 1 2 3 4 5 6 7 8 9 D3 ● × × × ● ● ● × × × dw ● D5 △ △ △ ● ● ● × × × what we want to do is １）Show that D3 brane (monopole) shorten the lifetime of the false vacuum ２）Propose a new method to construct a dielectric brane No Background Flux No Angular momentum D3 and DWD5 makes bound state 0 1 2 3 4 5 6 7 8 9 D3 ● × × × ● ● ● × × × dw D5 ● △ △ △ ● ● ● × × × from the true vacuum [ Hashimoto ’02] using dimensionless variables plot of energy vs radius of the bubble as b goes bigger 1)limit of existence of false vacuum 2)rmin is nonzero! rmin : r at local minimum bubble made at monopole has nonzero size!! fussy monopole Decay rate of Fuzzy brane How to calculate the decay rate? find the bounce euclidean action r 1）without monopole - O(4) symmetric bubble 2) with monopole - O(3) symmetric bubble most symmetric solution Decay rate of O(4) symmetric bubble： with thin wall approximation Φ ρ R ρ Decay rate of O(4) case WKB approximation thin wall approximation minimize B minimum B Decay of O(3) symmetric bubble Monopole/DW in Minkowski space ansatz of domainwall D5 brane “monopole case” internal space [Aganagic et al ’06] D3 brane dissolve into DWD5 and becomes a magnetic field B DBI action total action volume of internal space find bounce action use dimensionless variables euclideanize the action EOM is solve this about the “velocity” r impose bounce condition substitute the solution to the action estimate this value numerically plot of Bo(3)/Bo(4) vs b with monopole → lifetime becomes much shorter! another “character” with fundamental string attaching the bubble → topology change of the bubble Let’s turn on an electric field naively with spherical ansatz. action can be imaginary !! Spherical ansatz was incorrect for small bubble [Nishioka-Takayanagi 08] Pointing vector → angular momentum → bubble blows up along the string → eventually becomes a “doughnut” We assume bubble changes the topology to the doughnut. torus ansatz rewrite with D use dimensionless variables plot of energy vs width of the doughnut Potential has a minimum at nonzero width because of the angular momentum “Bo2” vs b as d goes higher compare the torus case to the previous monopole case length of the torus relation So, when Bo(2) is larger than Bo(3) topology change stabilize the bubble also, warping factor affect the lifetime drastically assume almost constant(for simplicity) corrections Bo(4) is corrected The lifetime is very long! in O(3) (monopole) case, the result is opposite... DBI action is corrected So,we replace the factor (in the previous result) and critical b is almost all b satisfy this bound → O(3) bubble is almost unstable! true vacua (not vacuum ,vacua) inside the bubble Actually, there are multiple SUSY true vacua inside the bubble. future work include gravitational and thermal effects. ● ランドスケープにおいて真空の寿命はもはやポテン シャルの形だけを用いた評価では正しくない ● Impurityの存在やwarp factorの存在が劇的に真空 の崩壊を早める ● どの点がランドスケープのアトラクターになるかの重 要な役割を果たすのではないか？